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

`vec(A)= 2hat(i)+2hat(j)-hat(k)` and `vec(B)= 6hat(i)-3hat(j)+2hat(k)`
`vec(C )= vec(A)xxvec(B)=(2hat(i)+2hat(j)-hat(k))xx(6hat(i)-3hat(j)+2hat(k))`
`=|(hat(i),hat(j),hat(k)),(2,2,-1),(6,-3,2)|= hat(i)-10hat(j)-18hat(k)`
Unit vector perpendicular to both `vec(A)` and vec(B)` =(hat(i)-10hat(j)-18hat(k))/(sqrt(1^(2)+10^(2)+18^(2)))=(hat(i)-10hat(j)-18hat(k))/(5sqrt(17))`