What is the unit vector that is orthogonal to the plane containing # ( i - 2 j + 3 k) # and # ( - 4 i - 5 j + 2 k) #?
The unit vector is
Firstly, we need the vector perpendicular to other two vectros:
For this we do the cross product of the vectors:
The cross product
We can check that they are perpendicular by doing the dot prodct.
The unit vector
The modulus of
So the unit vector is