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Question

Find the unit vector perpendicular to each of the vector a+b and ab, where a=3^i+2^j+2^k and b=^i+2^j2^k

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Solution

We can write a+b=4^i+4^j,ab=2^i+4^k
In order to find unit vector perpendicular to both a+b and ab, cross product of a+b and ab has to be determined.
det^i^j^k440102
= ^i(8)^j(8)+^k(4)
The unit vector is given as 4(2^i+2^j+^k)64+64+16=13(2^i+2^j+^k)



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