What is the x value of if it is rotated 45 degrees on the z axis, and 45 degrees on the y axis.?

Question

Alright this question will help me answer something. You have a line right starting at the origin and ending at (1,0) (think unit circle). you rotate it 45 counter clockwise on the Z axis so that its new coordinates are (sqrt2/2, sqrt2/2). Now suppose your rotate it another 45 degrees but this time on the Y axis. I'm having a hard time picturing this and think that the new coordinates would be either (sqrt2/4, sqrt2/2) or (1/2,sqrt2/2). Could someone please tell me which one of these if correct and if its neither what the correct x value is.

Answer 1

If you are considering 3 dimensions, will you please explain what (1,0) is?

How can you go on giving coordinates of a pint in 3-D as a point in 2-D?

does it make any sense?

Answer 2

For solving these types of rotation problems, use vectors.

You dont have to picture it hard, that will not solve the problem, you have to apply the concepts of vectors while picturing it.

Starting point : 1, 0, 0 = 1 = cos (0).i + cos (90). j + cos (90). k

Rotating around z-axis (add 45 to x and y components),  cos (45).i + cos (45). j + cos (90). k  = 1/√2, 1/√2, 0.

Rotating around y axis, (add 45 to x and z components)

cos (90).i + cos (45). j + cos (135). k

Final answer is

= 0 , 1/√2, -1/√2

Now you have understood the concept and method. Enjoy.