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Vector Algebra

Short Answer Type

61. Find the direction cosines of the vector joining the points A (1, 2, – 3) and B (– 1, – 2. 1). directed from A to B.

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62. If A is (a₁ , a₂ , a₃),

AB with rightwards arrow on top

is vector

straight b with rightwards arrow on top space equals space straight b subscript 1 straight i with hat on top space plus space straight b subscript 2 straight j with hat on top space plus space straight b subscript 3 straight k with hat on top

, find the coordinates of B.

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63.

If $PQ with rightwards arrow on top space equals space 3 straight i with hat on top space plus space 2 straight j with hat on top space minus space straight k with hat on top$ and the coordinates of P are (1, – 1, – 2), find the coordinates of Q.

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64. Find the values of x and y so that the vectors $2 straight i with hat on top space plus space 3 straight j with hat on top$ and $straight x straight i with hat on top space plus space straight y straight j with hat on top$ are equal.

Since $2 straight i with hat on top plus space 3 straight j with hat on top$ and $straight x straight i with hat on top space plus space straight y straight j with hat on top$ are equal
$therefore$ their corresponding components are equal
$therefore space space space space straight x space equals space 2 comma space space space straight y space equals space 3.$

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65.

Let $straight a with rightwards arrow on top space equals space straight i with hat on top space plus space 2 space straight j with hat on top$ and $straight b with rightwards arrow on top space equals space 2 straight i with hat on top space plus space straight j with hat on top.$ Is $open vertical bar straight a with rightwards arrow on top close vertical bar space equals space open vertical bar straight b with rightwards arrow on top close vertical bar space ?$ Are the vectors $straight a with rightwards arrow on top space and space straight b with rightwards arrow on top$ equal?