   Chapter 12.4, Problem 31E

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.31. P(0, −2, 0), Q(4, 1, −2), R(5, 3, 1)

(a)

To determine

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

Explanation

Given:

P(0,2,0),Q(4,1,2) and R(5,3,1) .

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(0,2,0),Q(4,1,2) and R(5,3,1) .

Find PQ .

PQ=Q(4,1,2)P(0,2,0)=(40),(1+2),(20)=4,3,2

Find PR

(b)

To determine

To find: The area of triangle PQR.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find more solutions based on key concepts 