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Vector Algebra

Question
CBSEENMA12033999
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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.

Solution

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.

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