1_e. Please give step by step answer. Only do part e. Let P = (-2,0, 5), Q(3, 1, 1), and R = (0,0,4)and define a =PÓ and b = PŘ. Find(d) The equation of the plane which passes through P, Q, and R.(e) The distance between the plane found in part (d) and the point (6, 2, – 1).

Step:-1 Given that P=-2, 0, 5, Q=3, 1, 1, R=0, 0, 4 PQ→=3-(-2), 1-0, 1-5=5, 1, -4PQ→=5, 1,…

Answered: Let P = (-2,0, 5), Q = (3, 1, 1), and R…

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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1_e. Please give step by step answer. Only do part e.

Let P = (-2,0, 5), Q
(3, 1, 1), and R = (0,0,4)
and define a =
PÓ and b = PŘ. Find
(d) The equation of the plane which passes through P, Q, and R.
(e) The distance between the plane found in part (d) and the point (6, 2, – 1).

Expert Solution

Step 1

Step:-1

Given that $P = (- 2, 0, 5), Q = (3, 1, 1), R = (0, 0, 4)$

$\vec{P Q} = <3 - (- 2), 1 - 0, 1 - 5> = <5, 1, - 4> \vec{P Q} = <5, 1, - 4> \vec{P R} = <0 - (- 2), 0 - 0, 4 - 5> = <2, 0, - 1> \vec{P R} = <2, 0, - 1> n o r m a l v e c t o r \hat{n} = \vec{P Q} \times \vec{P R} \hat{n} = |\begin{matrix} i & j & k \\ 5 & 1 & - 4 \\ 2 & 0 & - 1 \end{matrix}| \hat{n} = i (- 1 - 0) - j (- 5 + 8) + k (0 - 2) = <- 1, - 3, - 2>$

So, the equation of plane is ( For this take any one point from P, Q, R)

$\Rightarrow - 1 (x - 0) - 3 (y - 0) - 2 (z - 4) = 0 \Rightarrow x + 3 y + 2 z - 8 = 0$

This is the required plane.

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