What is the unit vector perpendicular to the following vectors `2hati+2hatj-hatk` and `6hati-3hatj+2hatk`

Options

A. `(hati+10hatj-18hatk)/(5sqrt(17))`
B. `(hati-10hatj+18hatk)/(5sqrt(17))`
C. `(hati-10hatj-18hatk)/(5sqrt(17))`
D. `(hati+10hatj+18hatk)/(5sqrt(17))`

Answer

C

Explanation

(c ) `A=2hati+2hatj-hatkand 6hati -3hatj+2hatk`
`t=|underset(6" "-3" "2)overset(""hati" "hatj" "hatk)underset( " "2" "2" "-1)""|`
`hati (4-3)-hatj (4+6) +hatk (-6-12) `
`=hati-10hatj-18hatk`
Unit vector perpendicular to both A and B
`=(hati-10hatj-18hatk)/(sqrt((1)^2)+(10)^(2)+(18)^(2))=(hati-10hatj-18hatk)/(5sqrt(17))`