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Unformatted text preview: A reection in R 3 through a plane P is the transformation that leaves the points of P xed 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 reection. For a plane P through the origin in R 3 , the reection through P is given by the following formula. Let be a unit vector perpendicular to P . For any x 2 R 3 , the reection j of x through P is given by j . x / D x 2 h x ; i , where h ; i denotes the inner product in R 3 . In the Exercises, you are asked to verify this formula and to compute the matrix of a reection, with respect to the standard basis of R 3 . You are...
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- Fall '08