It's given vector $\vec{e_{1}}=0.31\vec{e_{x}}+0.95\vec{e_{y}}$. How do I rotate that for 30 degrees counterclokwise? What I have done, I have used $x’=x\cos\theta-y\sin\theta$, $y’=x\sin\theta+y\cos\theta$, but I'm not sure if get right solution.
How do I rotate vector?
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vector-spaces
vectors
rotations
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2Check to see if $\vec e_i \cdot \vec e'_i=\cos(\pi/6)$ for $i=x,y$. – 2017-02-25
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1It's correct. To convince yourself, try drawing a picture. – 2017-02-25
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0@Dr.MV What exactly theta should be? – 2017-02-26
1 Answers
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Given a point $p=(x,y)$, you can rotate it $\theta$ degrees to get a point $\tilde{p}$ by using the rotation matrix $R\in\mathbb{R}^{2\times2}$ via $$ \tilde{p} = Rp = \begin{bmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} $$ which rotates $p$ counterclockwise by $\theta$ degrees.
Notice that your results are exactly as given here :) Check out this wiki too.