Question

Let `veca = hati + hatj, vecb = hati - hatj` and `vecc = hati + hatj + hatk`. If `hatn` is a unit vector such that `veca.hatn` = 0 and `vecb.hatn` = 0, then find `|vecc.hatn|`.

Answer 1

Given, `veca = hati + hatj, vecb = hati - hatj`

and `vecc = hati + hatj + hatk`

Also, given `veca.hatn` = 0

and `vecb.hatn` = 0

Here, `hatn = (veca xx vecb)/(|veca xx vecb|)`

Here, `veca xx vecb = |(hati, hatj, hatk),(1, 1, 0),(1, -1, 0)|`

= `hati(0 - 0) - hatj(0 - 0) + hatk(-1 - 1)`

= `-2hatk`

∴ `hatn = (-2hatk)/sqrt((-2)^2) = - hatk`

Therefore, `|vecc.hatn| = |(hati + hatj + hatk).(-hatk)|`

= |–1|

= 1