Question

Find two unit vectors each of which is perpendicular to both `baru` and `barv` where `baru = 2hati + hatj - 2hatk`, `barv = hati + 2hatj - 2hatk`.

Answer 1

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)`