In order to find perpendicular vectors in three dimensions, you need to know how to find the determinant of a matrix and how to find the cross product of two vectors.
Step 1 Allow a general form for three vectors
For the purposes of this article, a =, b = and c = where c is perpendicular to both a and b.
Step 2 Know the definition of the cross product
The cross product will give a vector c that is perpendicular to both a and b.
Step 3 Find the cross product of a and b
- i(a2b3-a3b2)-j(a1b3-a3b1)+k(a1b2-a2b1)
Step 4 Put in component form
<(a 2 b 3 -a 3 b 2 ), -(a 1 b 3 -a 3 b 1 ), (a 1 b 2 -a 2 b 1 )>
Tips
- You need either one vector and a point or two vectors to use this method.
- If you are given one vector and one point, you will need to find a second vector using the components of the vector and the ordered triple of the point.
- If you are only given one vector, come up with another point in the plane so you can find a second vector b.
- Remember that you can insert a "k" as a scalar to find all parallel vectors to c.
