Unformatted text preview: A reﬂection in R 3 through a plane P is the transformation that leaves the points of P ﬁxed and sends a point x 62 P to the point on the line through x and perpendicular to P , which is equidistant from P with x and on the opposite side of P . Figure 4.3.1. A reﬂection. For a plane P through the origin in R 3 , the reﬂection through P is given by the following formula. Let ˛ be a unit vector perpendicular to P . For any x 2 R 3 , the reﬂection j ˛ of x through P is given by j ˛ . x / D x ± 2 h x ;˛ i ˛ , where h² ; ²i denotes the inner product in R 3 . In the Exercises, you are asked to verify this formula and to compute the matrix of a reﬂection, with respect to the standard basis of R 3 . You are...
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
- Fall '08