Question

Question #ed3e7

Answer 1

`-12hati+10hatj-28hatk`

Explanation:

A vector that is perpendicular to two vectors is their cross product

if

`veca=a_1hati+a_2hatj+a_3hatk`

`vecb=b_1hati+b_2hatj+b_3hatk`

then a perpendicular vector is

`veca xx vecb` which is calculated by the determinant

`veca xx vecb=|(hati,hatj,hatk), (a_1,a_2,a_3),(b_1,b_2,b_3)|`

in this case

`veca xx vecb=|(hati,hatj,hatk),(4,2,-1),(2,-6,-3)|`

now expand

`=hati|(2,-1),(-6,-3)|-hatj|(4,-1),(2,-3)|+hatk|(4,2),(2,-6)|`

`=hati(-6-6)-hatj(-12+2)+hatk(-24-4)`

`=-12hati+10hatj-28hatk`