Question
Asked Dec 8, 2019
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Consider the points below.
P(0, -3, 0), Q(6, 1, -2), R(6, 2, 1)
(a) Find a nonzero vector orthogonal to the plane through the points P,
Q, and R.
(b) Find the area of the triangle PQR.
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Consider the points below. P(0, -3, 0), Q(6, 1, -2), R(6, 2, 1) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. (b) Find the area of the triangle PQR.

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Step 1

P(0,-3,0) , Q(6,1,-2), R(6,2,1)

Find two vectors on the plane PQ and PR 

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PQ =Q-P =(6,1,-2)-(0,-3,0) =(6,4,-2) PR =R-P =(6,2,1)-(0,-3,0) =(6,5,1)

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Step 2

Cross product of PQ and PR produces a vector orthogonal to the tw...

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(a,b,c)x(d,e,f) =(bf-ce,cd-af,ae-bd) (6,4,-2)×(6,5,1) =(4+10,-12-6,30-24) =(14,-18,6)

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