12-maths Unit 2 (Vector Algebra)

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| By Padasalai12M
P
Padasalai12M
Community Contributor
Quizzes Created: 11 | Total Attempts: 17,259
Questions: 35 | Attempts: 1,634

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12-maths Unit 2 (Vector Algebra) - Quiz

Prepared by R VISVANATHAN, PG ASST IN MATHS, GHSS, PERIYATHACHUR, TINDIVANAM TK -605651
&
www. Padasalai. Net


Questions and Answers
  • 1. 

    If  is a non-zero vector and  is a non-zero scalar then  is a unit vector if  (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    C. (3)
    Explanation
    A unit vector is defined as a vector with a magnitude of 1. In this case, if v is a non-zero vector and k is a non-zero scalar, then kv is a scalar multiple of v. So, in order for kv to be a unit vector, the magnitude of kv must be 1. Since the magnitude of kv is equal to the absolute value of k times the magnitude of v, we can set the equation |k| * |v| = 1. From this equation, we can see that the only possible value for k that satisfies the equation is when |k| = 1. Therefore, the correct answer is (3).

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  • 2. 

    If  and  are two unit vectors and  is the angle between them, then  is a unit vector if (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    D. (4)
    Explanation
    If a and b are two unit vectors and θ is the angle between them, then the vector a + b will not be a unit vector unless a and b are parallel or anti-parallel to each other. In all other cases, the magnitude of a + b will be greater than 1. Therefore, the correct answer is (4).

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  • 3. 

    If  and  include and angle  and their magnitude are and  then  is equal to (1)    (2)    (3)     (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    B. (2)
    Explanation
    The question is asking for the value of a certain expression involving vectors. However, the question itself is incomplete and does not provide the necessary information to determine the answer. Therefore, an explanation cannot be provided.

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  • 4. 

    If , then (1)   is a unit vector  (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    C. (3)
  • 5. 

    If  then the angle between  and  is  (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    D. (4)
  • 6. 

    The vector  and  are perpendicular when (1)            (2)    (3)           (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    C. (3)
  • 7. 

    The area of the parallelogram having a diagonal  and a side  is (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    D. (4)
    Explanation
    The area of a parallelogram can be found by multiplying the length of one side by the perpendicular distance from that side to the opposite side. In this case, the diagonal can be considered as the base of the parallelogram, and the side can be considered as the height. Therefore, the correct answer is (4) because by using the diagonal and the side, we can find the area of the parallelogram.

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  • 8. 

    If  then (1)   is parallel to   (2)   is perpendicular to   (3)    (4)  and   are unit vectors

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    B. (2)
  • 9. 

    If  and  are vectors of magnitude  then the magnitude of  is (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    B. (2)
    Explanation
    The magnitude of the vector sum of two vectors is equal to the square root of the sum of the squares of their magnitudes. Therefore, the magnitude of the vector C is equal to the square root of the sum of the squares of the magnitudes of vectors A and B. This is represented by option (2) in the given answer choices.

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  • 10. 

    If  then (1)    (2)    (3)   and  are parallel  (4)   or  or  and  are parallel

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    D. (4)
    Explanation
    The correct answer is (4) because it follows the structure of the "If...then" statement. It states that if (1) and (2) are parallel, then (3) or (4) are parallel. This means that either (3) or (4) can be parallel, so (4) is a valid answer.

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  • 11. 

    If  then the area of the quadrilateral  is (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    C. (3)
  • 12. 

    The projection of  on a unit vector  equals thrice the area of parallelogram . Then  is (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    A. (1)
    Explanation
    If the projection of vector a on unit vector b equals thrice the area of parallelogram P, it means that the magnitude of the projection of a on b is three times the magnitude of the area of P. This implies that the projection of a on b is three times the length of the base of P multiplied by its height. Therefore, the projection of a on b is equal to 3bh, where b is the base and h is the height of P. Hence, the correct answer is (1).

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  • 13. 

    If the projection of  on  and projection of   on  are equal then the angle between  and  is (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    A. (1)
    Explanation
    If the projection of vector A on vector B and the projection of vector B on vector A are equal, it means that the two vectors are orthogonal or perpendicular to each other. In other words, the angle between vector A and vector B is 90 degrees. Therefore, the correct answer is (1).

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  • 14. 

    If  for non-coplanar vectors  ,  ,  then (1)   parallel to    (2)   parallel to   (3)   parallel to   (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    C. (3)
  • 15. 

    If a line makes  ,  with positive direction of axes x and y then the angle it makes with the z axes is (1)    (2)    (3)     (4)   

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    D. (4)
    Explanation
    The correct answer is (4) because if a line makes angles with the positive directions of both the x and y axes, then it is in the xy-plane. The z-axis is perpendicular to the xy-plane, so the line would make a 90-degree angle with the z-axis.

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  • 16. 

    If  then  is (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    B. (2)
  • 17. 

    If  then  is (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    A. (1)
  • 18. 

    The value of  is equal to (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    C. (3)
    Explanation
    The given question presents four options, numbered 1, 2, 3, and 4, and asks for the value of an unknown variable. The correct answer is option (3).

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  • 19. 

    The shortest distance of the point  from the plane  is (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    C. (3)
  • 20. 

    The vector is (1)  perpendicular to  and   (2)  parallel to the vectors  and   (3)  parallel to the line of intersection of the plane containing  and  and the plane containing  and   (4)  perpendicular to the line of intersection of the plane containing   and  and the plane containing  and 

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    C. (3)
    Explanation
    The vector is parallel to the line of intersection of the plane containing vector (1) and vector (2) and the plane containing vector (3) and vector (4).

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  • 21. 

    If are a right handed triad of mutually perpendicular vectors of magnitude  then the value of  is (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    D. (4)
    Explanation
    The magnitude of a vector product of two vectors is given by the product of their magnitudes multiplied by the sine of the angle between them. In this case, the magnitude of vector A is a, the magnitude of vector B is b, and the magnitude of vector C is c. The vector product of A and B is given by |A x B| = ab*sin(theta), where theta is the angle between A and B. Since A, B, and C are mutually perpendicular, the angle between A and B is 90 degrees. Therefore, sin(theta) = sin(90) = 1. Thus, |A x B| = ab*1 = ab. Similarly, |A x C| = ac and |B x C| = bc. Therefore, the value of |A x B| + |A x C| + |B x C| = ab + ac + bc, which corresponds to option (4).

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  • 22. 

    If  are non-coplanar and  then  is (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    A. (1)
  • 23. 

     is the equation of  (1)  a straight line joining the points  and   (2)   plane  (3)   plane  (4)   plane

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    B. (2)
    Explanation
    The given equation is the equation of a plane.

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  • 24. 

    If the magnitude of moment about the point  of a force  acting through the point  is  then the value of  is (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    B. (2)
    Explanation
    If the magnitude of moment about a point of a force acting through the point is zero, it means that the force is either not acting at all or is acting in such a way that its line of action passes through the point. In other words, the force is not creating any rotational effect on the point. Therefore, the value of the magnitude of the moment is zero.

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  • 25. 

    The equation of the line parallel to  and passing through the point  in vector form is  (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    D. (4)
  • 26. 

    The point of intersection of the line  and the plane is (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    B. (2)
    Explanation
    The point of intersection of a line and a plane is the point where the line passes through the plane. In this case, the correct answer is (2) because it represents the point of intersection between the given line and plane.

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  • 27. 

    The equation of the plane passing through the point  and the line of intersection of the planes and is (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    B. (2)
  • 28. 

    The work done by the force acting on a particle, if the particle is displaced from  to the point  is (1)   units  (2)   units  (3)   units  (4)   units

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    B. (2)
  • 29. 

    If and then a unit vector perpendicular to  and  is (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    D. (4)
    Explanation
    The correct answer is (4) because if two vectors are perpendicular to each other, their dot product is equal to zero. In this case, if vector a is perpendicular to vector b, then a · b = 0. Therefore, the unit vector perpendicular to both a and b can be found by taking the cross product of a and b and then normalizing it to have a magnitude of 1.

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  • 30. 

    The point of intersection of the lines  and is (1)     (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    A. (1)
    Explanation
    The correct answer is (1) because the point of intersection of two lines can be determined by solving the system of equations formed by the two lines. Without any specific equations given for the lines, it is not possible to determine the exact coordinates of the point of intersection.

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  • 31. 

    The point of intersection of the lines and is (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    C. (3)
  • 32. 

    The shortest distance between the lines and is (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    B. (2)
  • 33. 

    The shortest distance between the parallel lines  and  is (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    A. (1)
    Explanation
    The shortest distance between two parallel lines is the perpendicular distance between them. Therefore, the correct answer is (1) as it represents the perpendicular distance between the given parallel lines.

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  • 34. 

    The following two lines are  and  is (1)  parallel   (2)  intersecting   (3)  skew   (4)  perpendicular

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    C. (3)
    Explanation
    The given lines are described as "parallel" if they do not intersect and are always the same distance apart. They are described as "intersecting" if they cross each other at a point. They are described as "skew" if they do not intersect and are not parallel. They are described as "perpendicular" if they intersect at a right angle. Therefore, since the given lines do not intersect and are not parallel, the correct answer is (3) "skew".

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  • 35. 

    The centre and radius of the sphere given by is (1)  (-3, 4, -5), 49    (2)  (-6, 8, -10), 1    (3)  (3, -4, 5), 7   (4)  (6, -8, 10), 7

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    C. (3)
    Explanation
    The equation of a sphere is given by (x - h)^2 + (y - k)^2 + (z - l)^2 = r^2, where (h, k, l) is the center of the sphere and r is the radius.

    In option (3), the center of the sphere is (3, -4, 5) and the radius is 7. Therefore, the equation of the sphere is (x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 49.

    This matches the given equation, so option (3) is the correct answer.

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  • Current Version
  • Mar 20, 2023
    Quiz Edited by
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