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Question

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

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Solution

Given, a=^i+^j+^k and b=^i+2^j+3^k

a+b=2^i+3^j+4^k and ab=^j2^k

A vector which is perpendicular to both (a+b) and (ab) is given by,
(a+b)×(ab)=∣ ∣ ∣^i^j^k234012∣ ∣ ∣
=2^i+4^j2^k (=c, say)

Now, |c|=4+16+4=24=26

Therefore, the required unit vector is,
c|c|=16^i+26^j16^k

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