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Question

Let a=^i+^j+^k,b and c=^j^k be three vectors such that a×b=c and ab=1. If the length of projection vector of the vectorb on the vector a×c is l, then the value of 3l2 is equal to

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Solution

Given: a×b=c
(a×b)c=|c|2=2
Also, a×c=∣ ∣ ∣^i^j^k111011∣ ∣ ∣=2^i+^j+^k|a×c|=6
Now required length of projection
l=∣ ∣b(a×c)|a×c|∣ ∣=26
Hence, 3l2=2

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