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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 18E

(a)

To determine

To find:The set of parametric equations.

(a)

Expert Solution

Answer to Problem 18E

Theset of parametric equations are x=−32+32t , y=32−132t and z=2−12t .

Explanation of Solution

Given information:The points are (−32,32,2) and (0,−5,32) .

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=〈0+32,−5−32,32−2〉=〈32,−132,−12〉

So, the normal vector is v=〈32,−132,−12〉 and point on the plane is (−32,32,2) .

Substitute −32 for x1 and 32 for a in the equation x=x1+at .

x=−32+32t

Substitute 32 for y1 and −132 for b in the equation y=y1+bt .

y=32−132t

Substitute 2 for z1 and −12 for c in the equation z=z1+ct .

z=2−12t

Therefore, the set of parametric equations are x=−32+32t , y=32−132t and z=2−12t .

(b)

To determine

To find:The set of symmetric equations for the line passes through the two points (−32,32,2) and (0,−5,32) .

(b)

Expert Solution

Answer to Problem 18E

Theset of symmetric equation is x+3/23/2=y−3/2−13/2=z−2−1/2 .

Explanation of Solution

Given information:The points are (−32,32,2) and (0,−5,32) .

Calculation:

The normal vector is v=〈32,−132,−12〉 and point on the plane is (−32,32,2) .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+3/23/2=y−3/2−13/2=z−2−1/2

Therefore, the set of symmetric equation is x+3/23/2=y−3/2−13/2=z−2−1/2 .

Chapter 10.4, Problem 17E

Chapter 10.4, Problem 19E

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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