a. Explanation Given: As shown in figure here, N → is the normal to the plane p and L is the line that intersect p . The normal N → and the line L are N → = a i + b j + c k , and L : x = x 0 + A t , y = y 0 + B t , z = z 0 + C t . We find cos ϕ , ϕ = 90 0 − θ , θ is the angle between a given line and the plane. Method Used: Ifa , b , c and A , B , and C are the direction ratios of two lines then the angle between them β is given by cosβ= a A + b B + c C . Calculations: The normal to the plane is N → = a i + b j + c k , i.e., the direction ratios of the normal to the plane are a , b , c . The given line L : x = x 0 + A t , y = y 0 + B t , z = z 0 + C t can be written as x − x 0 A = y − y 0 B = z − z 0 C = t , i.e., the direction ratios of the line are A , B , and C . Thus, the line is parallel to the vector L → = A i + B j + C k As clear from the figure ϕ is the angle between line L and the normal N → b. To determine To find : The angle between a line and the plane.

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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Chapter 9.6, Problem 41PS

To determine

To find: The value of cosϕ , ϕ=900−θ , θ is the angle between a given line and the plane.

To determine

To find: The angle between a line and the plane.

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Chapter 9.6, Problem 40PS

Chapter 9.6, Problem 42PS

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

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The value of cos ϕ , ϕ = 90 0 − θ , θ is the angle between a given line and the plane.

Solution Summary: The author calculates the value of mathrmcosvarphi and the angle between a given line and plane.