Let  and  Is  Are the vectors  equal? from Mathematics
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    Vector Algebra

    Multiple Choice QuestionsShort 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.
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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?

    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 comma space space space 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
                       open vertical bar straight a with rightwards arrow on top close vertical bar space equals space square root of left parenthesis 1 right parenthesis squared plus left parenthesis 2 right parenthesis squared end root space equals space square root of 1 plus 4 end root space equals space square root of 5 open vertical bar straight b with rightwards arrow on top close vertical bar space equals space square root of left parenthesis 2 right parenthesis squared plus left parenthesis 1 right parenthesis squared end root space equals space square root of 4 plus 1 end root space equals space square root of 5
    therefore space space space space space space 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
    straight a with rightwards arrow on top space and space straight b with rightwards arrow on top are not equal as their corresponding components are distinct.
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    66. Find a unit vector in the direction of straight a with rightwards arrow on top space equals space 3 space straight i with hat on top space minus space 2 space straight j with hat on top space plus space 6 space straight k with hat on top.
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    67. Find unit vector in the direction of vector straight a with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space 3 space straight j with hat on top space plus space straight k with hat on top.
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    68. Find the unit vector in the direction of the sum of the vectors straight a with rightwards arrow on top space equals space 2 straight i with hat on top space plus space 2 space straight j with hat on top space minus space 5 space straight k with hat on top space and space space 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 space plus 3 space straight k with hat on top
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    69. If straight a with rightwards arrow on top space equals space 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 space and space straight b with rightwards arrow on top space equals space 3 straight i with hat on top space plus space straight j with hat on top space minus space 5 space straight k with hat on top comma find a unit vector in the direction of straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top.
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    70. Find the unit vector in the direction of the vector straight a with rightwards arrow on top space equals space straight i with hat on top space plus space straight j with hat on top space plus space 2 space straight k with hat on top.
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