the velocity of a wave is given by the vector <7,3>. FInd the direction of the vector to the nearest degree

Question

<7,3>. find the direction of the vector to the nearest degree

Answer 1

I am assuming this is a calc III question.  If it is one from say electromagnetics, or anything involving omega's and the like, I believe you would need a frequency or wavelength to solve this.  So, proceeding with the Calc III solution:

 

the vector <x,y>'s direction is represented by the relationship:

 

tanθ=y/x or θ=tan^-1(y/x)

 

θ=tan-1(3/7) ≈ θ Radians or degrees depending on your calculator's mode setting.

 

Or θ Radians * (180/pi) ≅ θ degrees.  

 

The magnitude of the vector, the actual velocity is calculated by taking the square root of the sum of the squares of the x and y components:

 

√(7)²+(3)² = √58

 

Which means all together, the velocity has a magnitude of √58 in the direction θ degrees from the positive x axis (assuming you are in cartesian coordinates).