a) Find a and c so that (a, 1, c) is a point on the line through (0, 2, 3) and Justify your answer. (2,7,5). b) Find the equation of the line through the point (2, 1, 1) and perpendicular to the vectors i +j+k and i + 2k. Give another point on this line.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 29E
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Question
Solve a and b part only Q1
a)
Find a and c so that (a, 1, c)
is a point on the line through (0, 2, 3) and
(2,7,5). Justify your answer.
b)
Find the equation of the line
through the point (2, 1, 1) and
perpendicular to the vectors i+j+ k and
i + 2k. Give another point on this line.
c) [
Find the equation of the plane
through the point (5, 1, 0) which is parallel
to the lines x = 2 + t, y = -2t, z = 1
and x = s, y = 2-s, z = 2 - 3s.
Provide detailed justification.
Transcribed Image Text:a) Find a and c so that (a, 1, c) is a point on the line through (0, 2, 3) and (2,7,5). Justify your answer. b) Find the equation of the line through the point (2, 1, 1) and perpendicular to the vectors i+j+ k and i + 2k. Give another point on this line. c) [ Find the equation of the plane through the point (5, 1, 0) which is parallel to the lines x = 2 + t, y = -2t, z = 1 and x = s, y = 2-s, z = 2 - 3s. Provide detailed justification.
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