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

Options

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

Answer

C

Explanation

`vec(A) = 2i + 2j - k , vec(B) = 6 i - 3 j + 2k`
`vec(A) xx vec(B) = |(I , j , k ) , (2 , 2 , -1), ( 6 , -3 , 2)| = i - 10 j - 18 k`
`|vec(A) xx vec(B)| = sqrt((1)^(2) + ( - 10)^(2) + (- 18)^(2)) = sqrt( 425) = 5 sqrt(17)`
Unit vector along `(vec(A) xx vec(B))/(|vec(A) xx vec(B)|) = ( i - 10 j - 18 k)/( 5 sqrt(17))`