# What is the unit vector that is orthogonal to the plane containing # (-i + j + k) # and # (3i + 2j - 3k) #?

##### 1 Answer

#### Answer:

There are two unit vectors here, depending on your order of operations. They are

#### Explanation:

When you take the cross product of two vectors, you are calculating the vector that is orthogonal to the first two. However, the solution of

As a quick refresher, a cross-product of

and you get each term by taking the product of the diagonal terms going from left to right, starting from a given unit vector letter (i, j, or k) and subtracting the product of diagonal terms going from right to left, starting from the same unit vector letter:

For the two solutions, lets set:

Let's look at both solutions:

#vecAoxvecB#

As stated above:

#vecBoxvecA#

As a flip to the first formulation, take the diagonals again, but the matrix is formed differently:

Notice that the subtractions are flipped around. This is what causes the 'Equal and opposite' form.