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Vector Algebra

Short Answer Type

71. For given vectors,

straight a with rightwards arrow on top space equals space 2 space straight i with hat on top space minus space straight j with hat on top space plus space 2 space straight k with hat on top space and space straight b with rightwards arrow on top space equals space minus straight i with hat on top space plus space straight j with hat on top space minus space straight k with hat on top comma space

find the unit vector in the direction of the vector

straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top

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72.

If $straight a with rightwards arrow on top space equals straight i with hat on top space plus space straight j with hat on top space plus space straight k with hat on top$ , $straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space minus space straight j with hat on top space plus space 3 space straight k with hat on top$ and $straight c with rightwards arrow on top space equals space straight i with hat on top space minus space 2 space straight j with hat on top space plus space straight k with hat on top$ , find a vector parallel to the vector $2 space straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top space plus space 3 space straight c with rightwards arrow on top$ .

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73. Find a vector in the direction of vector

5 space straight i with hat on top space minus space straight j with hat on top space plus space 2 space straight k with hat on top

which has magnitude 8 units.

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74. Find a vector of magnitude 5 units, and parallel to the resultant of the vectors

straight a with rightwards arrow on top space equals space 2 straight i with hat on top space plus space 3 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 straight i with hat on top space minus space 2 space straight j with hat on top space plus space straight k with hat on top.

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75. Show that the vectors $2 space straight i with hat on top minus 3 space straight j with hat on top space plus 4 space straight k with hat on top$ and $negative 4 space straight i with hat on top space plus space 6 space straight j with hat on top space minus space 8 space straight k with hat on top$ are collinear.

Let $straight a with rightwards arrow on top space equals space 2 space straight i with hat on top space minus space space 3 space straight j with hat on top space plus space 4 space straight k with hat on top$
and $straight b with rightwards arrow on top space equals space minus 4 space straight i with hat on top space plus space 6 space straight j with hat on top space minus space 8 space straight k with hat on top space equals space minus 2 left parenthesis 2 space straight i with hat on top space minus space space 3 space straight j with hat on top space plus space 4 space straight k with hat on top right parenthesis$
$therefore space space space space space straight b with rightwards arrow on top space equals space minus 2 straight a with rightwards arrow on top rightwards double arrow space space space space space straight a with rightwards arrow on top space equals space fraction numerator negative space 1 over denominator 2 end fraction straight b with rightwards arrow on top$
$therefore$ $straight a with rightwards arrow on top space and space straight b with rightwards arrow on top$ are collinear.