(a) Explanation Given information: It is provided a point P ( − 1 , 1 , 4 ) and a plane 2 x + 5 y − z = 3 Formula used: Skew lines are two (or more) lines which non-parallel but cannot meet. Imagine you are sitting in a room facing a wall. The top horizontal ceiling line in front of you and the bottom floor line on your right hand side is an example of two skew lines. The vertical line between the front wall and the side wall on your right is the shortest distance between these skew lines Calculation: To find the distance first, find the vector to the plane and for that we need to find a point on the plane, let us suppose x = 0 , y = 0 then we get z = − 3 thus ( 0 , 0 , − 3 ) is a point on the plane , thus we compute the vector from the point to the plane as [ − 1 1 4 ] − [ 0 0 − 3 ] = [ − 1 1 1 ] The shortest distance from a point to a plane is along the orthogonal to the plane , that is it is in the direction of normal vector Let n = [ 2 5 − 1 ] and v = [ − 1 1 1 ] then, v (b) To determine To find: The distance from the point P ( 4 , 5 , 0 ) to the plane x − 2 3 = y 5 = z + 1 − 1 . (c) To determine To find: The distance between the skew lines x = t , y = 2 t , z = 3 t − 1 and x = 1 − t , y = t + 2 , z = t .

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Question

Chapter 9, Problem 26PE

(a)

To determine

To find: The distance from the point P(−1,1,4) to the plane 2x+5y−z=3 .

(b)

To determine

To find: The distance from the point P(4,5,0) to the plane x−23=y5=z+1−1 .

(c)

To determine

To find: The distance between the skew lines x=t,y=2t,z=3t−1 and

x=1−t,y=t+2,z=t .

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Chapter 9, Problem 25PE

Chapter 9, Problem 27PE

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Chapter 9 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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The distance from the point P ( − 1 , 1 , 4 ) to the plane 2 x + 5 y − z = 3 .

Solution Summary: The author explains that skew lines are two (or more) lines which are non-parallel but cannot meet. The shortest distance is along the orthogonal to the plane.

Concept explainers

Videos

To find: The distance from the point P(−1,1,4) to the plane 2x+5y−z=3 .

To find: The distance from the point P(4,5,0) to the plane x−23=y5=z+1−1 .

To find: The distance between the skew lines x=t,y=2t,z=3t−1 and

x=1−t,y=t+2,z=t .

Want to see the full answer?

Chapter 9 Solutions

The distance from the point P ( − 1 , 1 , 4 ) to the plane 2 x + 5 y − z = 3 .

Solution Summary: The author explains that skew lines are two (or more) lines which are non-parallel but cannot meet. The shortest distance is along the orthogonal to the plane.

Concept explainers

Videos

To find: The distance from the point P(−1,1,4) to the plane 2x+5y−z=3 .

To find: The distance from the point P(4,5,0) to the plane x−23=y5=z+1−1 .

To find: The distance between the skew lines x=t,y=2t,z=3t−1 and x=1−t,y=t+2,z=t .

Want to see the full answer?

Chapter 9 Solutions

To find: The distance between the skew lines x=t,y=2t,z=3t−1 and

x=1−t,y=t+2,z=t .