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In relation to vectors, lines and planes.(a) Do the lines x/3=y/2=z/2 and x/5=y/3=(z-4)/2 intersect?(b) Find equations for a line perpendicular to both of these lines.(c) What is the distance between these lines?

Question

In relation to vectors, lines and planes.

(a) Do the lines x/3=y/2=z/2 and x/5=y/3=(z-4)/2 intersect?

(b) Find equations for a line perpendicular to both of these lines.

(c) What is the distance between these lines?

 

check_circleAnswer
Step 1

 (a) Given equations of the lines are,

(z-4)
Z
-and
5 3
3 2 2
2
Assume,
(z-4)
Aand
3 2 2
5 3
2
implies that,
x 3, 2,z 21
and
x 5, y 3
2u 4
help_outline

Image Transcriptionclose

(z-4) Z -and 5 3 3 2 2 2 Assume, (z-4) Aand 3 2 2 5 3 2 implies that, x 3, 2,z 21 and x 5, y 3 2u 4

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Step 2

Equating the coefficient of x, y, z from both equations,

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Step 3

on solving 1st two equ...

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