Determining Propagation vector from E(x,y,t)

[priceless]

Homework Statement

E(x,y,t)=(2i/sqrt(5)) + (j/sqrt(5)) Eo cos( 2pi(1/lamda)[2x/sqrt(5) - y/sqrt(5)]-[ft] )

Homework Equations

I Know k =2pi/lamda for 1D wave
I know K vetor=k dot r
I know K vector shows the direction of propogation, and must be perpendicular to E and B.

The Attempt at a Solution

Got 1/3 points on this part of my exam.
Kvector=2pi (1/lamda) [2/sqrt(5) - 1/sqrt(5)] * (2i/sqrt(5)) + (j/sqrt(5))
I know I have to check for normalizaton, and it is normalized.

Obviously this is wrong. I'm not sure how to define k for a multi dimensional wave, and my textbook does not show any example problems for 3 dimensional waves., or shows solutions for any multidimensional waves that involve K.Is the answer simply the resultant vector of kx and ky?
sqrt( (2/sqrt(5))^2 + (1/sqrt(5))^2)) which just equals sqrt(1)=1.

Edit: Referred back to Griffiths electrodynamics, and think I Figured it out.

K vector = K * r = (2pi/lamda) ( 2x^ / sqrt(5) - 1y^ / sqrt(5))
where x^ and y^ indicate the unit vectors xhat and yhat, not x to a power of ____.

 

[maajdl]

What is your question?
I don't see what the problem statement is.
Also what are the meaning of those i and j, are those things quaternions?
What is the meaning of [ft]?
Four us and for yourself, take a little bit more time to explain your question properly.

 

[priceless]

Apologies, it was determine the propagation vector from this equation of a plane-polarized wave.

 

[BvU]

Within the cosine, you see something that depends on x,y and something that depends on t.
Propagation has something to do with following time development of points (lines, planes) with constant E through time. $cos(\vec k \cdot \vec r - \omega t)$ I seem to remember.

 

[paranormal]

Yes, you are correct. The propagation vector, also known as the wave vector, is defined as K = 2π/λ * (n_x * x^ + n_y * y^ + n_z * z^), where n_x, n_y, and n_z are the components of the unit vector in the direction of propagation. In this case, since the wave is only propagating in the x-y plane, the z component can be ignored. The unit vectors x^ and y^ indicate the direction of the x and y axes, respectively. Therefore, the correct answer for the propagation vector in this case would be K = (2π/λ) * (2x^/√5 - y^/√5). It is important to note that the propagation vector is perpendicular to the electric and magnetic fields, as you mentioned.