Can a plane reflection in 3-space be written as the product of 3 line reflections?
My guts say the answer is No. Don't just tell me that my guts are right because the determinant of a plane reflection is -1 but the determinant of any line reflection, and so too any product of line reflections, is +1. This presupposes that the plane and the three lines all pass through the origin ... which may not be the case! Or, at least an argument would need to be given why the general case reduces to this special case.
10
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
1.6K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 140 views
- $30.00
Related Questions
- Why if $\frac{opp}{adj} =x$, then $x \times hyp =$ The length of a line perpendicular to the hypotenuse with the same height.
- Figure 1 shows two points A and B with a straight line drawn through them.
- Help finding the internal angles of my bike frame
- Land area calculation/verification
- Geometric Representation Question
- Geometric Representation Problem
- Find the volume of the solid obtained by rotating $y=x^2$ about y-axis, between $x=1$ and $x=2$, using the shell method.
- Find the area of the shaded region
Wunderbar! The demonstration is valid!!
You're welcome. Thanks for the coffee.