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

1 Answer
Jan 14, 2017

Answer:

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>#