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I am struggling to understand the 3D rotation. enter image description here

The initial object position is A(x1,y1,z1). We need rotate it into A′(x2,y2,z2) about z-axis by angle θ.And we take P be the any point in z-axis. It makes ∠APS=ϕ.

Now we find cosϕ=PS/OP=x1/r⇒x1=rcosϕ. But we know OQ=x1 but here slides take PS=x1 and match the answer.

My question is slides has wrong or my concepts is wrong? If both are wrong so how we find 3D rotation about any coordinate axis?

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    $\begingroup$ How is this related to graphic design? $\endgroup$
    – Wolff
    Oct 29 '21 at 16:14
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The dotted vector which ends to A(x1,y1,z1) and has length r does not start from the origin, it starts from P. The drawing visualizes rotation around Z-axis. It doesn't affect the Z-coordinate of the rotated point. Everything should be calculated with the XY-plane projection of the point. Here a copy of XY plane is placed to point P.

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