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Question

If a =i^+j^+k^, b =2i^-j^+3k^ and c =i^-2j^+k^,find a unit vector parallel to 2 a -b +3 c.

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Solution

We have, a= i^+j^+k^, b= 2i^-j^+3k^ and c= i^-2j^+k^
2a-b+3c = 2i^+j^+k^ - 2i^-j^+3k^+ 3i^-2j^+k^ = 3i^-3j^+2k^.

A unit vector parallel to 2a-b+3c is given by 2a-b+3c2a-b+3c=3i^-3j^+2k^32+-32+22
= 3i^-3j^+2k^22 =322i^-322j^+222k^

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