a=1 b=41)Find the vector and parametric scalar equations of the line L. Show that Q does not lieon L. 2)Without performing any numerical calculations, express d in terms of sin(θ) and |P Q| andhence show that d = |P Q × v(v with a hat)|. Proceed to use your points P and Q and the vector v(hat) to find d. 3)Find the point R such that PR =(P Q · v(hat)/|v(hat)| 2⃗ ) * v(hat). Confirm that R lies on the line L. Interpret the vector P R. Finally, verify that d = |RQ|. P(a,5,-2), Q = (3,0,b) and = +47-2kbe two points and a vector in R³ respectively. Let L be a line passing through P and paralleto v, and d be the shortest distance from Q to L. A general picture of this (not drawn to scale)is given below (note: is the acute angle line PQ makes with L):0PL

Step 1: Step 2: Step 3: Step 4: Would you mind marking the solution as useful on Course Hero if it…

P(a,5,-2), Q = (3,0,b) and = +47-2k be two points and a vector in R³ respectively. Let L be a line passing through P and paralle to v, and d be the shortest distance from Q to L. A general picture of this (not drawn to scale) is given below (note: is the acute angle line PQ makes with L): 0 P L

P(a,5,-2), Q = (3,0,b) and = +47-2k be two points and a vector in R³ respectively. Let L be a line passing through P and paralle to v, and d be the shortest distance from Q to L. A general picture of this (not drawn to scale) is given below (note: is the acute angle line PQ makes with L): 0 P L

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.3: Lines And Planes

Problem 31EQ

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Question

a=1 b=4
1)Find the vector and parametric scalar equations of the line L. Show that Q does not lie
on L.
2)Without performing any numerical calculations, express d in terms of sin(θ) and |P Q| and
hence show that d = |P Q × v(v with a hat)|. Proceed to use your points P and Q and the vector v(hat) to find d.

3)Find the point R such that PR =(P Q · v(hat)/|v(hat)| ²⃗ ) * v(hat). Confirm that R lies on the line L. Interpret the vector P R. Finally, verify that d = |RQ|.