Given = (8,−4,1) + t(4, 4, −2), find the point where the line intersects the plane with equation z + 7 = 0.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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6.
Given 7: = (8,−4,1) + t(4, 4, −2), find the point where the line intersects the
plane with equation z + 7 = 0.
Transcribed Image Text:6. Given 7: = (8,−4,1) + t(4, 4, −2), find the point where the line intersects the plane with equation z + 7 = 0.
Expert Solution
Step 1: Given

Equation space of space line space colon space straight r space equals space open parentheses 8 comma space minus 4 comma space 1 close parentheses space plus space straight t space space space open parentheses 4 comma space 4 comma space minus 2 close parentheses
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space open parentheses space 8 plus 4 straight t space comma space minus 4 plus 4 straight t space comma space 1 minus 2 straight t space close parentheses
Plane space colon space straight z plus 7 space equals space 0

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