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Question
Find two unit vectors each of which is perpendicular to both `baru` and `barv` where `baru = 2hati + hatj - 2hatk`, `barv = hati + 2hatj - 2hatk`.
Solution
Let `baru = 2hati + hatj - 2hatk, barv = hati + 2hatj - 2hatk`
Then `baru xx barv = |(hati ,hatj ,hatk),(2, 1, -2),(1, 2, -2)|`
= `(-2 - (-4))hati - (-4 - (-2))hatj + (4 - 1)hatk`
= `(-2 + 4)hati - (-4 + 2)hatj + 3hatk`
= `2hati + 2hatj + 3hatk`
∴ `|baru xx barv| = sqrt((2)^2 + (2)^2 + (3)^2)`
= `sqrt(4 + 4 + 9)`
= `sqrt(17)`
= `±(baru xx barv)/(|baru xx barv|)`
= `±( 2hati + 2hatj + 3hatk)/sqrt17`
= `±(2/sqrt17hati + 2/sqrt17hatj + 3/sqrt17hatk)`
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