# How do you find a unit vector that is orthogonal to a and b where #a = −7 i + 6 j − 8 k# and #b = −5 i + 6 j − 8 k#?

##### 1 Answer

The answer is

#### Explanation:

To find a vector orthogonal to 2 other vectors, we must do a cross product.

The cross product of 2 vectors,

is given by the determinant

and

Here, the 2 vectors are

And the cross product is

Verification, by doing the dot product

Therefore, the vector is perpendicular to the other 2 vectors

The unit vector isobtained by dividing by the modulus.

The modulus is

The unit vector is