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

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Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter10: Analytic Geometry

Section10.CT: Test

Problem 22CT

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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|.