Homework SourseCompute the orthogonal projection of v 1 3 3 onto the line
Compute the orthogonal projection of v = [-1 -3 -3] onto the line L through [4 4 -5] and the origin.![Compute the orthogonal projection of v = [-1 -3 -3] onto the line L through [4 4 -5] and the origin.SolutionLet P be the point (4,4,-5) and let O be the origin](/WebImages/6/compute-the-orthogonal-projection-of-v-1-3-3-onto-the-line-988665-1761508140-0.webp "Compute the orthogonal projection of v = [-1 -3 -3] onto the line L through [4 4 -5] and the origin.SolutionLet P be the point (4,4,-5) and let O be the origin")
Solution
Let P be the point (4,4,-5) and let O be the origin i.e. (0,0,0) . Then the vector urepresenting the line OP ( or, L ) is (4,4,-5) - (0,0,0) = (4, 4,-5). The orthogonal projection of v = ( -1,-1,-3) on u = (4, 4, -5) is proju (v) = [ <v, u>/ < u,u>] u = [( v. u )/( u.u )] u = [ ( -4 -4 +15)/( (16+16+ 25)] ( 4,4,-5) = 7/57 ( 4,4,-5) = (28/57, 28/57,-35/57)
