What is the unit vector perpendicular to the following Vector `2hat(i)+2hat(j)-hat(k)` and `6hat(i)-3hat(j)+2hat(k)?`

Options

A. `(hat(i)+10hat(j)-18hat(k))/(5sqrt(17))`
B. `(hat(i)-10hat(j)+18hat(k))/(5sqrt(17))`
C. `(hat(i)-10hat(j)-18hat(k))/(5sqrt(17))`
D. `(hat(i)+10hat(j)+18hat(k))/(5sqrt(17))`

Answer

C

Explanation

(c)`A=2hat(i)+2hat(j)-hat(k)andB=6hat(i)-3hat(j)+2hat(k)`
`C=AxxB=|{:(hat(i),hat(j),hat(k)),(2,2,-1),(6,-3,2):}|`
`=hat(i)(4-3)-hat(j)(4+6)+hat(k)(-6-12)`
`=hat(i)-10hat(j)-18hat(k)`
Unit vector perpendicular to both A and B
`=(hat(i)-10hat(j)-18hat(k))/(sqrt((1)^(2)+(10)^(2)+(18)^(2)))=(hat(i)-10hat(j)-18hat(k))/(5sqrt(17))`