# What is the unit vector that is orthogonal to the plane containing # <3, 2, 1> # and # <1, 1, 1> #?

##### 1 Answer

Nov 10, 2016

The unit vector is

#### Explanation:

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

Therefore,