a is 1 and b is 1 Let P = = (4, 1, a), Q = (–2, 0, b) and v = i – 3j + 4k be two points and a vector inR³ respectively.(a) Write down the vector and parametric scalar equations of the line L passingthrough P parallel to v.(b) Show that your point Q does not lie on L.The shortest distance from a point to a line is the length of the line segment fromthat point meeting the line perpendicularly. A general (not to scale) picture of thisis given below:V→Pd =perpendicular distance from Q to LLet / be the angle between the vectors P and v.L(c) Without performing any numerical calculations, show thatd = |PQ × v|(d) Now calculate d with your specific points P and Q and line L. (You mayleave your answer in surd notation).(e) Find the point R on the line L such that QRcoordinates of your point R as fractions).=d. (You may give the

The given points are 4,1,a and -2,0,b. The given vector is v=i-3j+4k in ℝ3. The vector equation of…

Let P = (4, 1, a), Q = (-2, 0, b) and v=i − 3j + 4k be two points and a vector in R³ respectively. (a) Write down the vector and parametric scalar equations of the line L passing through P parallel to v. (b) Show that your point Q does not lie on L.

Let P = (4, 1, a), Q = (-2, 0, b) and v=i − 3j + 4k be two points and a vector in R³ respectively. (a) Write down the vector and parametric scalar equations of the line L passing through P parallel to v. (b) Show that your point Q does not lie on L.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.3: Lines And Planes

Problem 47EQ

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Question

a is 1 and b is 1

Let P = = (4, 1, a), Q = (–2, 0, b) and v = i – 3j + 4k be two points and a vector in
R³ respectively.
(a) Write down the vector and parametric scalar equations of the line L passing
through P parallel to v.
(b) Show that your point Q does not lie on L.
The shortest distance from a point to a line is the length of the line segment from
that point meeting the line perpendicularly. A general (not to scale) picture of this
is given below:
V
→
P
d =perpendicular distance from Q to L
Let / be the angle between the vectors P and v.
L
(c) Without performing any numerical calculations, show that
d = |PQ × v|
(d) Now calculate d with your specific points P and Q and line L. (You may
leave your answer in surd notation).
(e) Find the point R on the line L such that QR
coordinates of your point R as fractions).
=
d. (You may give the

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