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(a) Show that the point P(5,0,0) lies in the plane r + 2y + 6z = 5 and the point Q(1, –2, 4) does not. %3D (b) Find the scalar and vector projections of the vector PQ from (a) onto the vector 3 (1,2, 6). (c) Without any further calculation, find the distance from the point Q(1,-2,4) to the plane a+ 2y + 6z = 5. )0 a =

(a) Show that the point P(5,0,0) lies in the plane r + 2y + 6z = 5 and the point Q(1, –2, 4) does not. %3D (b) Find the scalar and vector projections of the vector PQ from (a) onto the vector 3 (1,2, 6). (c) Without any further calculation, find the distance from the point Q(1,-2,4) to the plane a+ 2y + 6z = 5. )0 a =

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.1: Length And Dot Product In R^n
Problem 17E: Consider the vector v=(1,3,0,4). Find u such that a u has the same direction as v and one-half of...
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(a) Show that the point P(5,0,0) lies in the plane r + 2y + 6z = 5 and the point Q(1, –2, 4) does not. %3D (b) Find the scalar and vector projections of the vector PQ from (a) onto the vector 3 (1,2, 6). (c) Without any further calculation, find the distance from the point Q(1,-2, 4) to the plane a+ 2y + 6z = 5. )0 a =
Transcribed Image Text:(a) Show that the point P(5,0,0) lies in the plane r + 2y + 6z = 5 and the point Q(1, –2, 4) does not. %3D (b) Find the scalar and vector projections of the vector PQ from (a) onto the vector 3 (1,2, 6). (c) Without any further calculation, find the distance from the point Q(1,-2, 4) to the plane a+ 2y + 6z = 5. )0 a =
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