What is the unit vector that is orthogonal to the plane containing # <3, 2, 1> # and # <1, 1, 1> #?
The unit vector is
To calculate a vector ortogonal to 2 other vectors, we caculate the cross product.
The cross product is the determinant of
So the vector ortogonal is
To verify, we do the dot products .
As the dot products are
To compute the unit vector, we divide by the modulus.
The modulus is