Vector Algebra

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| By Tanmay Shankar
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Tanmay Shankar
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Quizzes Created: 491 | Total Attempts: 1,857,291
| Attempts: 996 | Questions: 15
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About This Quiz
Vector Algebra - Quiz

This Vector Algebra quiz assesses skills in computing vector properties and solving vector-related problems. It includes questions on finding position vectors, unit vectors, and areas of triangles using vector methods, essential for learners aiming to master vector algebra concepts.

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5) Write unit vector in the direction of the sum of vectors: 

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7) Write the position vector of the mid-point of the vector joining the points P (2, 3, 4) and Q (4, 1, — 2).

Explanation

The position vector of the midpoint of the vector joining two points can be found by taking the average of the corresponding coordinates of the two points. In this case, the midpoint of the vector joining P(2, 3, 4) and Q(4, 1, -2) can be found by taking the average of the x-coordinates, y-coordinates, and z-coordinates. Therefore, the position vector of the midpoint is [(2+4)/2, (3+1)/2, (4+(-2))/2] = [3, 2, 1].

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8) Show that each of the given three vectors is a unit vector: Which of the following is true?

Explanation

The statement "All of these" means that each of the given three vectors is a unit vector. A unit vector is a vector with a magnitude of 1. Since the question states that all of the given vectors are unit vectors, it implies that each vector has a magnitude of 1, satisfying the definition of a unit vector. Therefore, the answer is correct.

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11) Using vectors, find the area of the triangle ABC with vertices A (1, 2, 3), B (2, -1, 4) and C (4, 5, -1). 

Explanation

To find the area of a triangle using vectors, we can use the cross product of two vectors formed by the sides of the triangle. The magnitude of the cross product gives us the area of the parallelogram formed by the two vectors, and dividing it by 2 gives us the area of the triangle.

In this case, we can find the vectors AB and AC by subtracting the coordinates of the respective points. Then, we can calculate the cross product of AB and AC. Taking the magnitude of the cross product and dividing it by 2 gives us the area of triangle ABC.

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14) P and Q are two points with position vectors and respectively. Write the position vector of a point R which divides the line segment PQ in the ratio 2:1 externally.

Explanation

The position vector of point R can be found by using the external division formula. According to the formula, the position vector of R is given by (2Q + 1P) / (2+1). This means that we multiply the position vector of Q by 2, the position vector of P by 1, and then add them together. Finally, we divide the result by the sum of the ratios, which is 2+1 = 3.

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Write unit vector in the direction of the sum of vectors: 
Write the position vector of the mid-point of the vector joining the...
Show that each of the given three vectors is a unit vector: ...
Using vectors, find the area of the triangle ABC with vertices A (1,...
P and Q are two points with position vectors and respectively. Write...
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