a) An aircraft, flying in a straight line, passes through the points (-6,7,2) and (-3,2,3) measured in kilometres. Find the vector form of the equation of the line that describes the flight path of the aircraft. Determine whether or not the aircraft is flying parallel to the ground which is described by the plane -4x + 6y + 42z = 17, where x.y and z are also measured in kilometres.
a) An aircraft, flying in a straight line, passes through the points (-6,7,2) and (-3,2,3) measured in kilometres. Find the vector form of the equation of the line that describes the flight path of the aircraft. Determine whether or not the aircraft is flying parallel to the ground which is described by the plane -4x + 6y + 42z = 17, where x.y and z are also measured in kilometres.
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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Transcribed Image Text:Question 2
a) An aircraft, flying in a straight line, passes through the points (-6,7,2) and (-3,2,3)
measured in kilometres. Find the vector form of the equation of the line that describes
the flight path of the aircraft. Determine whether or not the aircraft is flying parallel to
the ground which is described by the plane -4x + 6y + 42z = 17, where x.y and z are
also measured in kilometres.
b) A large shade sail is to be hung tautly between the tops of 3 poles. The tops of these
poles are located at point A, B, and C as shown in the Figure 1 below. For instance the
point A is located at (2, -3,3) m. find the vectors AB and AC and hence the equation of
the plane through these three points.
3 m
5 m
2 m
0
2 m
3 m
B
3 m
3 m
Figure 1: The poles in Q2(b) which the large shade sail is to be hung taughtly between.
c) A tunnel is being constructed through a mountain range where the tunnel is being
constructed from both ends at the same time. One end of tunnel starts at the point A
(80, -287, 106) and is constructed in a straight line in the direction 21 - 8j + 3k whilst
the other end of tunnel starts at the point B (-395,263, -89) and is constructed in a
straight line in the direction 91 - 6j + 2k. The starting points and the direction vectors
of both ends of the tunnel are measured in metres. Verify that the tunnels being
constructed from both ends meets by first finding the equations of both tunnels and
then finding their intersection point P.
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