2. The four points P(3, 1, 2), Q(1,0, 2), R(2, 1,0) and T(1, 1,-2) in R' lie on the same plane. (a) Find the vectors PQ, PŘ and PT. Then find a pair of linearly independent vectors among PQ, PŔ and PT. (b) Find the angle 0 between the two linearly independent vectors found in part (a). (c) Use your answers in part (a) to find an equation of the plane containing the points P Q, R and T in the standard form.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2.
The four points P(3, 1, 2), Q(1,0, 2), R(2, 1,0) and T(1, 1,-2) in R' lie on the same plane.
(a) Find the vectors PQ, PŔ and PT. Then find a pair of linearly independent vectors
among PQ, PŔ and PT.
(b) Find the angle 0 between the two linearly independent vectors found in part (a).
(c) Use your answers in part (a) to find an equation of the plane containing the points P Q, R
and T in the standard form.
Transcribed Image Text:2. The four points P(3, 1, 2), Q(1,0, 2), R(2, 1,0) and T(1, 1,-2) in R' lie on the same plane. (a) Find the vectors PQ, PŔ and PT. Then find a pair of linearly independent vectors among PQ, PŔ and PT. (b) Find the angle 0 between the two linearly independent vectors found in part (a). (c) Use your answers in part (a) to find an equation of the plane containing the points P Q, R and T in the standard form.
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