Explanation Given information: The equation of line are x = − 1 + t , y = − 2 t , z = 3 and line passing through the points ( 0 , − 1 , 2 ) & ( 1 , − 2 , 3 ) Concept and Formula Used: Distance between two lines is equal to the distance between the parallel planes containing them. To find the distance ‘d’ between two planes find the distance between a point on one plane to the other plane. d = ‖ A x 0 + By 0 +Cz 0 + D ‖ A 2 + B 2 + C 2 Equation of plane A ( x − x 0 ) + B ( y − y 0 ) + C ( z − z 0 ) = 0 Equation line passing from two points ( x 1 , y 1 , z 1 ) & ( x 2 , y 2 , z 2 ) is x − x 1 x 2 − x 1 = y − y 1 y 2 − y 1 = z − z 1 z 2 − z 1 Calculation: It is given that equation of lines are L 1 : x = − 1 + t , y = − 2 t , z = 3 & L 2 : x − 0 1 − 0 = y + 1 − 2 + 1 = z − 2 3 − 2 = t ( using x − x 1 x 2 − x 1 = y − y 1 y 2 − y 1 = z − z 1 z 2 − z 1 ) L 2 : x = t , y = − 1 − t , z = 2 + t Let line L 1 lie on plane p 1 , therefore any point ‘Q’ on plane p 1 : putting t = 0 in L 1 , Q ( − 1 , 0 , 3 ) Now, vectors parallel to line L 1 & L 2 are v 1 = 〈 1 , − 2 , 0 〉 & v 2 = 〈 1 , − 1 , 1 〉 respectively. Also, cross product of v 1 = 〈 1 , − 2 , 0 〉 & v 2 = 〈 1 , − 1 , 1 〉 i .e

6th Edition

ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Chapter 9.6, Problem 35PS

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To Find: Distance between lines x=−1+t,y=−2t,z=3 and line passing through the points (0,−1,2)&(1,−2,3)

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Chapter 9.6, Problem 34PS

Chapter 9.6, Problem 36PS

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Chapter 9 Solutions

Calculus

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Distance between lines x = − 1 + t , y = − 2 t , z = 3 and line passing through the points ( 0 , − 1 , 2 ) & ( 1 , − 2 , 3 )

Solution Summary: The author explains how to find the distance between two planes. The equation of lines is l

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To Find: Distance between lines x=−1+t,y=−2t,z=3 and line passing through the points (0,−1,2)&(1,−2,3)

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Chapter 9 Solutions

Distance between lines x = − 1 + t , y = − 2 t , z = 3 and line passing through the points ( 0 , − 1 , 2 ) &amp; ( 1 , − 2 , 3 )

Solution Summary: The author explains how to find the distance between two planes. The equation of lines is l

Concept explainers

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To Find: Distance between lines x=−1+t,y=−2t,z=3 and line passing through the points (0,−1,2)&(1,−2,3)

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Chapter 9 Solutions

Distance between lines x = − 1 + t , y = − 2 t , z = 3 and line passing through the points ( 0 , − 1 , 2 ) & ( 1 , − 2 , 3 )