True or False line and plane perpendicular The line : X =- 3t, y = 1 - 2t, z = 2 - tis perpendicular to the plane: X - y - z = 1.[g]

Answered: The line : X - 3t, y = 1 - 2t, z = 2 -…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 21E

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Question

True or False line and plane perpendicular

The line : X =
- 3t, y = 1 - 2t, z = 2 - tis perpendicular to the plane: X - y - z = 1.[g]

Expert Solution

Step 1

$G i v e n t h a t e q u a t i o n o f l i n e x = - 3 t, y = 1 - 2 t, z = 2 - t a n d e q u a t i o n o f p l a n e x - y - z = 1 T o c h a q u e t h e l i n e a n d p l a n e a r e p e r p e n d i c u l a r o r n o t S o l u t i o n : e q u a t i o n o f l i n e \frac{x}{- 3} = \frac{y - 1}{- 2} = \frac{z - 2}{- 1} = t e q u a t i o n o f p l a n e x - y - z = 1 d i c e c t i o n r a t i o o f l i n e (- 3, - 2, - 1) n o r m a l v e c t o r o f p l a n e (1, - 1, - 1) i f l i n e a n d p l a n e a r e p e r p e n d i c u l a r t h e n d i r e c t i o n r a t i o a r e s a m e$