Vector Algebra

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Question

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Question 1 :

If a, b and c be non-zero vectors, then which of the following statements is correct?

1. a x (b - c) = (c - b) x a
2. a ^. (b + c) = (c + b) ^. a
3. a x (b + c) = (c + b) x a
4. a ^. (b - c) = (c - b) ^. a
Answer
6931

Question 2 :

The area, of the parallelogram having diagonals
d₁ = 3 i + j - 2k and d₂ = i - 3j + 4k is

1. 10√3
2. 5√3
3. 8
4. 4
Answer
6932

Question 3 :

If position vectors of four points A, B, C and D are i + j + k, 2i + 3j, 3i + 5j - 2k and k - j respectively, then AB and CD are related as

1. perpendicular
2. parallel
3. independent
4. none of these
Answer
6933

Question 4 :

Consider four points P, Q, R and S with their position vector - (j + k), 4i + 5j + λk, 3i + 9j + 4k and - 4i + 4j + 4k, respectively. If |PQ| = |QR|, then λ is equal to ?

1. 1
2. - 1
3. 2
4. - 2
Answer
6934

Question 5 :

What is the vector perpendicular to both the vectors i - j and i?

1. i
2. - j
3. j
4. k
Answer
6935