Find the equation of the plane passing through the three points. P =(4,-1,8), Q = (1, 1, 1), R = (3, 1,-2) Consider the proposed solution for the equation of the line passing through all three points. Find n = QPX QR = (4 – 1,(-1) — 1,8 – 1) × (3 – 1,1 – 1,(−2) — 1) = (3, -2,7) × (2, 0, -3) i j k 7 -3 = 3 2 = -2 0 = (6,23,4) Then, n (x, y, z) = d where d = . = (3,-2, 7) · (2,0, -3) = -15 Therefore, the equation of the line is 6x + 23y + 4z = -15 OP OR Is this the correct equation of the line? If not, explain?
Find the equation of the plane passing through the three points. P =(4,-1,8), Q = (1, 1, 1), R = (3, 1,-2) Consider the proposed solution for the equation of the line passing through all three points. Find n = QPX QR = (4 – 1,(-1) — 1,8 – 1) × (3 – 1,1 – 1,(−2) — 1) = (3, -2,7) × (2, 0, -3) i j k 7 -3 = 3 2 = -2 0 = (6,23,4) Then, n (x, y, z) = d where d = . = (3,-2, 7) · (2,0, -3) = -15 Therefore, the equation of the line is 6x + 23y + 4z = -15 OP OR Is this the correct equation of the line? If not, explain?
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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Transcribed Image Text:Find the equation of the plane passing through the three points.
P =(4,-1,8), Q = (1, 1, 1),
R=(3, 1,-2)
Consider the proposed solution for the equation of the line passing through all three points.
Find n = =OP XOR
= (4 – 1, (−1) — 1, 8 − 1) × (3 – 1, 1 – 1, (−2) – 1)
= (3,-2,7) x (2,0, -3)
i
= 3 -2
2
0
j k
7
-3
=
= (6,23,4)
Then, n. (x, y, z) = d where d = OP OR
= (3,-2,7) (2,0,-3)
= -15
Therefore, the equation of the line is
6x + 23y + 4z = -15
Is this the correct equation of the line? If not, explain?
Transcribed Image Text:Is this the correct equation of the line? If not, explain?
The equation, 6x + 23y + 4z = −15 of the line is
because the
Equation of the line:
is
Find the equation of the line.
(Enter an exact answer. Use symbolic notation and fractions where needed. Enter the answer as an equation in the form
ax + by + cz = d.)
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