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) + 10 hat(j)- 18 hat(k))/(5 sqrt17)`
B. `(hat(i)- 10 hat(j) + 18 hat(k))/(5 sqrt17)`
C. `(hat(i)- 10 hat(j)- 18 hat(k))/(5 sqrt17)`
D. `(hat(i) + 10 hat(j) + 18 hat(k))/(5 sqrt17)`

Answer

C

Explanation

`vec(A) = 2 hat(i) + 2hat(j) - hat(k), B= 6hat(i)- 3hat(j) + 2hat(k)`
`vec(C) = vec(A) xx vec(B) = |(hat(i),hat(j),hat(k)),(2,2,-1),(6,-3,2)|= hat(i) - 10 hat(j)- 18 hat(k)`
Unit vector perpendicular to both `vec(A) and vec(B)`
`hat(C)= (vec(C))/(|vec(C)|)= (hat(i)- 10 hat(j)- 18 hat(k))/(sqrt(1^(2) + (-10)^(2) + (-18)^(2)))= (hat(i)- 10 hat(j)- 18 hat(k))/(5 sqrt17)`