A power cable is to be fitted under a road and can be represented on 3D Cartesian axes as below, with the x-axis pointing East, the y-axis North, and the z-axis vertical. The pipeline is to consist of a straight section AB directly under the road, and another straight section BC connected to the first. All lengths are in metres. fla, b, 0) A (0, -40, 0) x (E) (40, 0, -20) a. Evaluate the distance AB. The section BC is to be drilled in the direction of the vector 3i + 4j + k. b. Find the angle between the sections AB and BC. The section of pipe reaches ground level at the point C(a, b, 0). c. Write down a vector equation of the line BC. Hence find a and b.
A power cable is to be fitted under a road and can be represented on 3D Cartesian axes as below, with the x-axis pointing East, the y-axis North, and the z-axis vertical. The pipeline is to consist of a straight section AB directly under the road, and another straight section BC connected to the first. All lengths are in metres. fla, b, 0) A (0, -40, 0) x (E) (40, 0, -20) a. Evaluate the distance AB. The section BC is to be drilled in the direction of the vector 3i + 4j + k. b. Find the angle between the sections AB and BC. The section of pipe reaches ground level at the point C(a, b, 0). c. Write down a vector equation of the line BC. Hence find a and b.
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:A power cable is to be fitted under a road and can be represented on 3D Cartesian axes as below,
with the x-axis pointing East, the y-axis North, and the z-axis vertical. The pipeline is to consist
of a straight section AB directly under the road, and another straight section BC connected to
the first. All lengths are in metres.
Cla, b, 0)
A (0, -40, 0),
x (E)
B (40, 0, -20)
a. Evaluate the distance AB.
The section BC is to be drilled in the direction of the vector 3i + 4j + k.
b. Find the angle between the sections AB and BC.
The section of pipe reaches ground level at the point C(a, b, 0).
c. Write down a vector equation of the line BC. Hence find a and b.
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