I m doing an assignment and this is what is asks: (c) Find the sum of the squares of the cosines of the corresponding coordinate direction angles found above. (Measure the cosines of the corresponding coordinate direction angles from the x-y plane.)

Question

Im not quite sure what it is asking me to do. Part a and b got me to find angles alpha, beta and gamma for 2 vectors with the same magnitude but different directions.

If someone can explain to me what I should be doing that would be great. If you need the values or some other info let me know.
Thanks

Answer 1

I am sorry, I have no idea what these angles alpha, beta and gamma are for the two vectors. Are they in three dimensions and the angles to the x, y and z axes? In that case the three angles do not define the direction of a vector. The direction depends not only on the angle to the three axes but also the ORDER in which you do the rotations.

Answer 2

I bet it is 2 d
say angle alpha above x axis in xy plane
same vector is angle beta to y axis
call vector length h
then cos alpha = x/h and cos^2 = x^2/h^2
cos beta = y/h and cos^2 = y^2/h^2
sum = (x^2+y^2)/h^2
BUT
h is hypotenuse = sqrt(x^2 + y^2)
so we have h^2/h^2 = 1
perhaps this is what they mean.

Answer 3

Of course you could do that much more easily with geometry :)