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High School Math Calculus PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

The set of parametric equations.

The set of parametric equations.

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

8th Edition

ISBN: 9781337904285

Author: Larson

Publisher: CENGAGE L

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Question

Chapter 10.4, Problem 13E

(a)

To determine

To find:The set of parametric equations.

(a)

Expert Solution

Answer to Problem 13E

Theparametric equations are x=−3+4t , y=8−10t and z=15+t .

Explanation of Solution

Given information:The points are (−3,8,15) and (1,−2,16) .

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=〈1+3,−2−8,16−15〉=〈4,−10,1〉

So, the normal vector is v=〈4,−10,1〉 and point on the plane is (−3,8,15) .

Substitute −3 for x1 and 4 for a in the equation x=x1+at .

x=−3+4t

Substitute 8 for y1 and −10 for b in the equation y=y1+bt .

y=8−10t

Substitute 15 for z1 and 1 for c in the equation z=z1+ct .

z=15+t

Therefore, the parametric equations are x=−3+4t , y=8−10t and z=15+t .

(b)

To determine

To find:The set of symmetric equations for the line passes through the two points (−3,8,15) and (1,−2,16) .

(b)

Expert Solution

Answer to Problem 13E

Theset of symmetric equation is x+34=y−8−10=z−151 .

Explanation of Solution

Given information: The points are (−3,8,15) and (1,−2,16) .

Calculation:

The normal vector is v=〈4,−10,1〉 . It can be seen that the direction numbers are all non-zero.So, the set of symmetric equations can be calculated as:

x−x0a=y−y0b=z−z0cx+34=y−8−10=z−151

Therefore, the set of symmetric equation is x+34=y−8−10=z−151 .

Chapter 10.4, Problem 12E

Chapter 10.4, Problem 14E

Chapter 10 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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

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