#4. Let L be the line containing the vector [3]. Find the orthogonal projection of the vector1-41)onto L. (use the formula: proj L(x) = (x ⋅ u) u, where u is contained in L, ||u||x =-31√[2³].L4(Use the formula ref LX = 2 (xu) u x, where u is contained in L, ||u|| = 1)#5. Find the reflection of(A)31/2513/2517/25(B)Habout the line L in the direction of the vector31/250-17/25-(C)-31/250-17/25(D)31/25017/25(E) None of the above

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Answered: #4. Let L be the line containing the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose = [2, 1, −1]ª, ♂ = [1, −1, 1]ª and √ = [2,0, 1]T. Let W = Span{7,V}. (a) Find the best approximation to y by a vector of W. (b) Write ✅ y as the sum of a vector in W and a vector in W¹. (c) Find the distance between and W. (d) Let A = [√, √]. Note that Aỡ ‡ ☞ for all ☞ € R². Find min ||A7 J'||. TER²
#4. Let L be the line containing the vector [13]. Find the orthogonal projection of the vector -4 x = onto L. (use the formula: proj L(x) = (x u) u, where u is contained in L, ||u|| = 1) ·3 H about the line L in the direction of the vector 0 [4 (Use the formula ref LX = 2 (xu) u - x, where u is contained in L, ||u|| = 1) #5. Find the reflection of of (A) [31/25] 13/25 (B) 17/25 31/25 0 -17/25 (C) -31/25 0 -17/25 (D) 31/25 0 17/25 (E) None of the above
If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from a point P to the line L is equal to the length of the component of the vector AP that is orthogonal to the vector AB. P A B Use the method above to find the distance from the point P(-3, 1, 11) to the line through A(1, 1,0) and B(-2,3, –4). NOTE: Enter the exact answer. Distance
If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from a point P to the line L is equal to the length of the component of the vector AP that is orthogonal to the vector AB. P L B Use the method above to find the distance from the point P(-3,1, 12) to the line through A(1,1,0) and B(-2,3, –4). NOTE: Enter the exact answer. Distance = %3D

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#4. Let L be the line containing the vector Q or[3]. Find the orthogonal projection of the vector -31 x = onto L. (use the formula: proj L (x) = = (xu) u, where u is contained in L, ||u|| = 1)