Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let's say we have a vector $D=(\sqrt2, 0, 0)$ and we do the following operations on it.

1) Rotate it in the clockwise direction against the $X$ axis for $\pi/4$

2) Rotate it in the counter clockwise direction against the $Y$ axis for $\pi/4$

that's the vector $D1$, we then perform steps 1 & 2 but we reverse the order, i.e. 1 would be counter clockwise and 2 would be clockwise; that's vector $D2$.

What's the angle that $D$ forms with $D1$ and $D2$?

From my calculations if we rotate it for the same amount in both axis it would still retain the $\pi/4$ span against both cases would it not?

share|cite|improve this question

Hint : Use rotation matrix to determine the new position of the vectors . For example along $z$ axis $$x' = x \cos \theta - y \sin \theta$$ $$y' = x \sin \theta + y \cos \theta$$ $$z' = z$$ along $x$ axis $$y' = y\cos \theta - z \sin \theta$$ $$z' = y\sin \theta + z\cos \theta$$ $$x' = x$$ , where $ \theta$ is the angle and so on ...

share|cite|improve this answer
Well, I did the calculations and I am asking if the answer I got it correct... – jtimz Feb 9 '14 at 21:27

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.