How can I find an orthogonal vector?

This seems like it should be simple, but I haven't been able to figure out how to use Matlab to calculate an orthogonal vector.

If my vector is:

syms a 
p=[1;-a;0]

Then dot(p, the_orthogonal_vector) should = 0. But how can I calculate the orthogonal vector? I tried

help null

but couldn't see how to apply that to this.

[William]

The vector you gave is on the xy plane, therefore one of the orthogonal vectors is also on that plane. The formula for that is to transpose the x and y values and change the sign of one of them. For example, the vector u = [a;1;0] is orthogonal to p. v = [-a;-1;0] is also orthogonal. This is a special case where vectors on one of the primary planes, xy, xz, yz, can use the transpose and a sign change to find an orthogonal vector.

Answer 1

[David Goodmanson]

Hello Sue,

use null of the transpose of p:

syms a 
p=[1;-a;0]
n = null(p.')
n =
 
[ a, 0]
[ 1, 0]
[ 0, 1]

and each column of n is perpendicular to p, as is any linear combination of those two columns.