Q.
A unit vector perpendicular to i^−j^​+k^ and i^+j^​−k^ is
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J & K CETJ & K CET 2008Vector Algebra
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Solution:
Let a=i^−j^​+k^ and b=i^+j^​−k^
Now, a×b=∣∣​i^11​j^​−11​k^1−1​∣∣​ =i^(1−1)−j^​(−1−1)+k^(1+1) =2j^​+2k^ ∴ Required unit vector =±4+4​2j^​+2k^​ =±2​j^​+k^​