vector problems; a rod of length 2.6 is located at r =(19, 18, -19)m and held in position so that

Question

one end of the rod of length 2.6m is located at r= (19,18,-19)m and held in position so that the angle between the rod and the +x axis is 45 degrees, the angle between the rod and the +y axis is 49 degrees and the angle between the rod and the +z axis is 105 degrees what is the location of the far end of the rod

I tried the cos sign rule like cos(45) for all the degrees but that was wrong

would i do like cos(45-19) to get the right answer?

Answer 1

If you label the coordinates of the end of the vector as x,y,z, then the cosines of the angles between the vector and the x, y, z axes axis are cos θ_x = (x - 19) / 2.6, cos θ_y = (y - 18) / 2.6, and cos θ_z = (z + 19) / 2.6.

These equations have only one unknown each, so you should be able to calculate the unknowns which will be the coordinates of the rod's terminus.