# Electromagnetism Unit Vectors

## Homework Statement

I am having difficulty understanding the very first step of the following solved problem (I understand the rest of the solution).

How did they obtain the expressions for ##\hat{n}## (the direction of polarization), and ##\hat{k}## (the unit vector pointing in the direction of the wave vector)?

## Homework Equations

##k=\frac{\omega}{\lambda f} = \frac{\omega}{c}=\frac{2 \pi}{\lambda}##

##E(r, t) = E_0 \ cos (k.r - \omega t) \hat{n}##

##B(r,t) = \frac{1}{c} E_0 \ cos (k.r - \omega t) (\hat{k} \times \hat{n})##

## The Attempt at a Solution

What technique did they use to find the expression ##\frac{1}{\sqrt{6}} (\hat{x}+2\hat{y}+\hat{z})## for the unit vector perpendicular to ##x+y+z=0## plane?

Likewise, how did they get the expression ##\frac{1}{\sqrt{5}} (\hat{y}-2 \hat{z})## for the unit vector parallel to the y-z plane?

I could not find any explanations in my Linear Algebra textbook. So any explanation would be greatly appreciated.

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blue_leaf77
Homework Helper
Where do you get that solution from?

Where do you get that solution from?
This was the solution provided by my teacher. I don't understand, where did he get he get the expressions for ##\hat{n}## and ##\hat{k}## from?

blue_leaf77