Find a nonzero vector orthogonal to the plane through the points P, Q, and R. and area of the triangle PQR Consider the points below P(1,0,1) , Q(-2,1,4) , R(7,2,7) a) Find a nonzero vector orthogonal to the plane through the points P,Q and R b) Find the area of the triangle PQR

beljuA 2021-05-14 Answered
Find a nonzero vector orthogonal to the plane through the points P, Q, and R. and area of the triangle PQR
Consider the points below
P(1,0,1) , Q(-2,1,4) , R(7,2,7)
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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Expert Answer

saiyansruleA
Answered 2021-05-15 Author has 110 answers
Jeffrey Jordon
Answered 2021-09-08 Author has 2047 answers

a) The given vertices are P(1,0,1),Q(2,1,4) and R(7,2,7) is PQ(21,10,41)=(3,1,3), PK=(71,20,71)=(6,2,6)

The normal vector to the plane passing through the given three points is n=PQ×PR

=|ijk313626|

=(66)i(1818)j+(86)k

=(0)i+36j12k

=<0,36,12>

This normal vector is orthogonal to the plane throught the point P,Q,R

b) |PQ×PR|=02+362+(12)2=1296+144=1440

=1210

Area of the triangle with verties P,Q and R is

A=12|PQ×PR|

=12(1210)

=610

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