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High School Math Calculus Precalculus with Limits: A Graphing Approach

The set of parametric equations.

The set of parametric equations.

Precalculus with Limits: A Graphing Approach

Precalculus with Limits: A Graphing Approach

7th Edition

ISBN: 9781305071711

Author: Ron Larson

Publisher: Brooks/Cole

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Question

Chapter 10.4, Problem 18E

(a)

To determine

To find:The set of parametric equations.

(a)

Expert Solution

Answer to Problem 18E

Theparametric equations are x=2 , y=−1+2t and z=5−8t .

Explanation of Solution

Given information:The points are (2,−1,5) and (2,1,−3) .

Formula used: The parametric equations for the line parallel to vector v=〈a, b, c〉 and passing through the point (x1, y1, z1) are given by,

x=x1+at , y=y1+bt and z=z1+ct

Calculation:

The direction vector can be obtained by the given two points as:

v=〈2−2,1+1,−3−5〉=〈0,2,−8〉

So, the normal vector is v=〈0,2,−8〉 and point on the plane is (2,−1,5) .

Substitute 2 for x1 and 0 for a in the equation x=x1+at .

x=2+(0)t=2

Substitute −1 for y1 and 2 for b in the equation y=y1+bt .

y=−1+2t

Substitute 5 for z1 and −8 for c in the equation z=z1+ct .

z=5−8t

Therefore, the set of parametric equations are x=2 , y=−1+2t and z=5−8t .

(b)

To determine

To find:The set of symmetric equations for the line passes through the two points (2,−1,5) and (2,1,−3) .

(b)

Expert Solution

Answer to Problem 18E

Theset of symmetric equation of line is not possible.

Explanation of Solution

Given information:The points are (2,−1,5) and (2,1,−3) .

Calculation:

The normal vector is v=〈0,2,−8〉 and point on the plane is (2,−1,5) . It can be observed that the direction numbers are not all non-zero. So, the symmetric equation of line is not possible.

Therefore, the set of symmetric equation of line is not possible.

Chapter 10.4, Problem 17E

Chapter 10.4, Problem 19E

Chapter 10 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - Prob. 32E Ch. 10.1 - Prob. 33E Ch. 10.1 - Prob. 34E Ch. 10.1 - Prob. 35E Ch. 10.1 - Prob. 36E Ch. 10.1 - Prob. 37E Ch. 10.1 - Prob. 38E Ch. 10.1 - Prob. 39E Ch. 10.1 - Prob. 40E Ch. 10.1 - Prob. 41E Ch. 10.1 - Prob. 42E Ch. 10.1 - Prob. 43E Ch. 10.1 - Prob. 44E Ch. 10.1 - Prob. 45E Ch. 10.1 - Prob. 46E Ch. 10.1 - Prob. 47E Ch. 10.1 - Prob. 48E Ch. 10.1 - Prob. 49E Ch. 10.1 - Prob. 50E Ch. 10.1 - Prob. 51E Ch. 10.1 - Prob. 52E Ch. 10.1 - Prob. 53E Ch. 10.1 - Prob. 54E Ch. 10.1 - Prob. 55E Ch. 10.1 - Prob. 56E Ch. 10.1 - Prob. 57E Ch. 10.1 - Prob. 58E Ch. 10.1 - 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