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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.

Advanced Engineering Mathematics
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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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
Transcribed Image Text: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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