# Orthogonal vector

Grand

## Homework Statement

Construct a third vector which is orthogonal to the following pair and normalize all three vectors:
$$\underline{a}=(1-i,1,3i), \underline{b}=(1+2i,2,1)$$

## Homework Equations

$$\underline{c}.\underline{a}=0$$ and $$\underline{c}.\underline{b}=0$$ where c=(x y z)

## The Attempt at a Solution

Mentor
Your relevant equations are a good start, so use them.

Grand
The question is, how do we make a dot product when the vectors are complex? Is it the same way as real vectors or not?

Mentor
Do it the same way.

Homework Helper
Do it the same way.

Not exactly. You take the complex conjugate of the first vector before you multiply the components. Otherwise <x,x>>=0 doesn't work.

Apphysicist
Not exactly. You take the complex conjugate of the first vector before you multiply the components. Otherwise <x,x>>=0 doesn't work.

I'm not familiar with complex vectors, but since you want a vector that is orthogonal to both, rather than trying two dot products, wouldn't it be prudent to use a cross product?