Question

Find the unit vector perpendicular to each of the vectors `veca = 4hati + 3hatj + hatk` and `vecb = 2hati - hatj + 2hatk`.

Answer 1

Given, `veca = 4hati + 3hatj + hatk` and `vecb = 2hati - hatj + 2hatk`

Hence, `veca xx vecb = |(hati, hatj, hatk),(4, 3, 1),(2, -1, 2)|`

= `hati(6 + 1) - hatj(8 - 2) + hatk(-4 - 6)`

= `7hati - 6hatj - 10hatk`

Unit vector perpendicular to each at the vector `veca` and `vecb`

= `(veca xx vecb)/(|veca xx vecb|)`

= `(7hati - 6hatj - 10hatk)/sqrt((7)^2 + (-6)^2 + (-10)^2`

= `7/sqrt(185)hati - 6/sqrt(185)hatj - 10/sqrt(185)hatk`