Let $F$ be a reflection with respect to the plane defined by $2x + y = 0$, and let $G$ be the reflection with respect to the plane defined by $x + y - z = 0$. Show that the composition $F\circ G$ is a rotation and find $\cos(\theta)$ of the rotation.
Linear Algebra: Transformations
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linear-algebra
analytic-geometry
linear-transformations
rotations
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0What have you tried? Nobody wants to spoil your learning opportunity by simply typing out an answer for you. – 2017-01-04
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0I tried finding the matrix for both reflections and then composing them into one matrix and finding the determinant to show that if it was equal to one it would be rotation, but that didn't quite work out. – 2017-01-04
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0You didn't get a determinant of $1$? Because that should work. You can then get $\cos\theta$ from the trace (which is equal to $2\cos\theta+1$). – 2017-01-04
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0A reflected vector should be of the form $r'=r-2(r.n)n$ where n is a unit normal vector to the plane. Did you use that to calculate the F and G matrices? – 2017-01-04