Question

What is the unit vector that is orthogonal to the plane containing `<0, 4, 4>` and `<1, -1, 1>`?

Answer 1

Compute the cross product of the to vectors.
Compute the magnitude of the resulting vector.
Divide the resulting vector by its magnitude.
The unit vector is: `< sqrt(6)/3, sqrt(6)/6, -sqrt(6)/6>`

Explanation:

Compute the cross product:

#<0,4,4>xx <1,-1,1> = | (hati,hatj,hatk), (0,4,4), (1,-1,1) | = 8hati + 4hatj - 4hatk#

Compute the magnitude:

`r = sqrt(8^2 + 4^2 + (-4)^2)`

`r = sqrt(96) = 4sqrt(6)`

The unit vector is: `< sqrt(6)/3, sqrt(6)/6, -sqrt(6)/6>`