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  4. If a unit vector is represented by 0.5 hat i - 0 . 8 hatj + c hatk then the value of c is

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Q. If a unit vector is represented by $ 0.5 \hat{ i} - 0 . 8 \hat{j} + c \hat{k}$ then the value of c is

AIPMTAIPMT 1999Motion in a Plane

Solution:

For a unit vector $ \hat{n}$, $| \hat{n} | = 1 $
$|0.5 \hat{i} - 0.8 \hat{j} + c \hat{k} |^2 = 1^2$
$ \Rightarrow 0.25 + 0 .64 + c^2 = 1 $
or c = $ \sqrt{ 0.11}$