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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
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
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
Expert Solution
steps

Step by step

Solved in 3 steps

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,