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Suppose
a = ax i + ay j + az k
b = bx i + by j +bz k
Then
ab
= (aybz - azby) i + (azbx
- axbz) j + (axby -
aybx) k
(1,01)
(1,0,1) = 0;
(1,1,1)
(1,1,0) = (-1,1,0)
To check your answer: check that answer is orthogonal to each factor.