   Chapter 12.4, Problem 32E

Chapter
Section
Textbook Problem

# (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. and (b) find the area of triangle PQR.32. P(2, −3, 4) Q(−1, −2, 2), R(3, 1, −3)

(a)

To determine

To find: A nonzero vector orthogonal to the plane through the points P,Q and R .

Explanation

Given:

P(2,3,4),Q(1,2,2) and R(3,1,3) .

Formula:

Write the expression for cross product between a and b vectors.

a×b=|ijka1a2a3b1b2b3| (1)

The vectors PQ×PR is perpendicular to both PQ and PR , therefore perpendicular to the plane through P(2,3,4),Q(1,2,2) and R(3,1,3) .

Find PQ .

PQ=Q(1,2,2)P(2,3,4)=(12),(2+3),(24)=3,1,2

Find PR

(b)

To determine

To find: The area of triangle PQR.

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