Vectors Operations Quiz

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  • 1/10 Questions

    What has magnitude and direction?

    • Initial Point
    • Vector
    • Scalar
    • Terminal Point
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About This Quiz

Do you know about vector operations? Take this vectors operations quiz to find out how much you know about this concept. Here, we have got a few questions to test your knowledge of vector operations. Give this quiz a try to see your level of understanding of vector operations. Try to get a 100% score on this quiz. If you find this quiz helpful in your practice of vector operations, do not forget to share it with others.

Vectors Operations Quiz - Quiz

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  • 2. 

    If w = <2, -5> and y = <2, 0>, find 2w + y.

    • <-6, 10>

    • <-10, 2>

    • <4, -5>

    • <6, -10>

    Correct Answer
    A. <6, -10>
    Explanation
    The given question asks to find the value of 2w + y, where w = and y = . To find 2w, we multiply each component of w by 2, resulting in . Adding this to y, we get + = . Therefore, the correct answer is .

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  • 3. 

    Given u = <3, 7> and v =<-5, 4>, find 2u - 3v.

    • <-11, 26>

    • <21, 2>

    • 23

    • <8, 3>

    Correct Answer
    A. <21, 2>
    Explanation
    To find 2u - 3v, we need to multiply each component of u by 2 and each component of v by -3, and then subtract the corresponding components.

    For u = , multiplying each component by 2 gives us .
    For v = , multiplying each component by -3 gives us .

    Now, subtracting the corresponding components gives us = .

    Therefore, the correct answer is .

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  • 4. 

    Given v = <3,-5> and w = <-2,3>, what is 2v + 3w?

    • <6,10>

    • <1,1>

    • <-2,1>

    • <0,-1>

    Correct Answer
    A. <0,-1>
    Explanation
    To find 2v + 3w, we need to multiply each component of v by 2 and each component of w by 3, and then add the corresponding components together.

    2v = 2 * =
    3w = 3 * =

    Adding the corresponding components:
    2v + 3w = + = =

    Therefore, the correct answer is .

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  • 5. 

    If v =〈a,b〉, then a is the ___________ component of v.

    • Vertical

    • Horizontal

    • Slope

    • Parallel

    Correct Answer
    A. Horizontal
    Explanation
    If v = 〈a,b〉, then a is the horizontal component of v. This is because in a two-dimensional Cartesian coordinate system, the x-axis represents the horizontal direction. The vector v = 〈a,b〉 represents a displacement in the x-axis (horizontal direction) of a units and in the y-axis (vertical direction) of b units. Therefore, a represents the displacement in the horizontal direction, making it the horizontal component of v.

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  • 6. 

    If a turtle moves from coordinate P = (3,2) to Q = (5,6). Which vector models the turtle's motion?

    • <2,4>

    • <8,8>

    • <-1,5>

    • None of the above

    Correct Answer
    A. <2,4>
    Explanation
    The turtle moves from coordinate P = (3,2) to Q = (5,6). To find the vector that models the turtle's motion, we need to find the difference between the coordinates of Q and P. The x-coordinate of Q is 5 and the x-coordinate of P is 3, so the x-component of the vector is 5 - 3 = 2. Similarly, the y-coordinate of Q is 6 and the y-coordinate of P is 2, so the y-component of the vector is 6 - 2 = 4. Therefore, the vector that models the turtle's motion is .

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  • 7. 

    Find the magnitude of the vector <2, -3>.

    • √-4

    • 13

    • √13

    • √11

    Correct Answer
    A. √13
    Explanation
    The magnitude of a vector is calculated by taking the square root of the sum of the squares of its components. In this case, the vector has a magnitude of √(2^2 + (-3)^2) = √(4 + 9) = √13. Therefore, the correct answer is √13.

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  • 8. 

    Find the component form of a vector whose magnitude is 10 and direction is 150°.

    • <-5√3, -5>

    • <6.99 , -7.14>

    • 10i + 150j

    • <10, 150>

    Correct Answer
    A. <-5√3, -5>
    Explanation
    The correct answer is "<-5√3, -5>". This is the component form of a vector with a magnitude of 10 and a direction of 150 degrees. The first component, -5√3, represents the horizontal displacement of the vector, and the second component, -5, represents the vertical displacement.

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  • 9. 

    Find the angle between the two vectors <3, 4> and <4, -3>.

    • 45°

    • 90°

    • 53.13°

    • 106.26°

    Correct Answer
    A. 90°
    Explanation
    The angle between two vectors can be found using the dot product formula. The dot product of two vectors A and B is given by A · B = |A| |B| cosθ, where |A| and |B| are the magnitudes of the vectors and θ is the angle between them. In this case, the dot product of and is 3*4 + 4*(-3) = 12 - 12 = 0. Since the dot product is 0, the angle between the two vectors is 90°.

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  • 10. 

    Given vector u<-1,3,5> and v<3,y,z>, how much is y and z so the vectors are orthogonal.

    • Y=3,and z=-1

    • Y=-6,and z=3

    • Y=2, and z=2

    • Y=6,and z=-3

    Correct Answer
    A. Y=6,and z=-3
    Explanation
    To determine if two vectors are orthogonal, their dot product must be equal to zero.
    The dot product of u and v is given by -1(3) + 3(y) + 5(z).
    Setting this expression equal to zero and solving for y and z, we get 3y + 5z = 1.
    The only values of y and z that satisfy this equation are y = 6 and z = -3. Therefore, y = 6 and z = -3 make the vectors u and v orthogonal.

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  • Current Version
  • Sep 01, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Nov 02, 2022
    Quiz Created by
    Sophia Smith
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