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#1 2014-09-10 16:11:36

mrpace
Member
Registered: 2012-08-16
Posts: 88

Help with plane rotations??

Find a sequence of plane rotations that transform x = [6  6  17] to a multiple of [1  0  0].

Any ideas??

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#2 2014-09-10 20:04:18

Bob
Administrator
Registered: 2010-06-20
Posts: 10,052

Re: Help with plane rotations??

hi mrpace,

I'm still trying to fully understand what is expected here.  This is my thinking so far:

There must be a point which is the centre of the rotation.

The three points will define a single plane.  So why does the question ask for 'plane' rotations ?  This word seems to me to be redundant.

If this is from a linear algebra course that suggests the answer should be in the form of matrices.  Is that so ?

Transformation matrices must have the origin as an invariant point, so the centre would have to be at (0,0,0).

The distance to (6,6,17) can be calculated which fixes the radius of a single rotation.  There would be no more.

If we are to consider rotations where the centre is not at (0,0,0) , then you could call the centre (p,q,r) and form an equation using the equal radius distances.

Also, the centre will lie on the perpendicular bisector of the line joining (6,6,17) and (x,0,0).

Does that help ?

Bob


Children are not defined by school ...........The Fonz
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