Question

Find `|veca × vecb|`, if `veca = hati - 7hatj + 7hatk` and `vecb = 3hati - 2hatj + 2hatk`.

Answer 1

`veca = hati - 7hatj + 7hatk, vecb = 3hati - 2hatj + 2hatk`

`veca xx vecb = |(hati, hatj, hatk), (1, -7, 7), (3, -2, 2)|`

= `hati(-14 + 14) - hatj(2 - 21) + hatk(-2 + 21)`

= `19hatj + 19hatk`

∴ `|veca xx vecb| = sqrt((19)^2 + (19)^2)`

`= 19sqrt(1 + 1)`

`= 19sqrt2`.