Concept explainers
a.
If the line is perpendicular to the plane, find the relationship between
a.
Answer to Problem 36E
The
Explanation of Solution
Given information:
A line is parallel to the vector
Calculation:
Hence, it is given that vector
If the line is perpendicular to the plane, the vector
Hence the vector
b.
If the line is parallel to the plane, find the relationship between
b.
Answer to Problem 36E
Vector
Explanation of Solution
Given information:
A line is parallel to the vector
Calculation:
We know that the vector
Hence, if the line is parallel to the plane, then the vector
c.
Find the parallel and perpendicular line to the plane.
c.
Answer to Problem 36E
The vector
The vectors
Explanation of Solution
Given information:
A line is parallel to the vector
Prove line is parallel to the plane
Calculation:
Consider ,
We know that a line passing through the point
Compare the line
With standard parametric equations of a line, find the line is passing through
On comparing the line
With standard parametric equations of a line, find the line is passing through
Compare the plane
Two vectors are said to be parallel, if one vector is the scalar multiply of other vector.
We see that
Hence, the vector
Since, line
Two vectors are said to be perpendicular, if their dot product is zero.
The dot product of vectors
The dot product of vectors
Hence, the vectors
Hence, the line
plane
Chapter 9 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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