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Chapter 9: Q. 50 (page 627)

In Problems 49鈥�52, find the area of the parallelogram with vertices P1,P2,P3,P4

role="math" localid="1646760204418" P1=2,1,1P2=2,3,1P3=-2,4,1P4=-2,6,1

Short Answer

Expert verified

The area of the parallelogram is8 square units.

Step by step solution

01

Step 1. Given data

Vertices of the parallelogram are P1=2,1,1P2=2,3,1P3=-2,4,1P4=-2,6,1

The area of the Parallelogram is the magnitude of the cross product of the adjacent sides.

A=u脳v

02

Step 2. Finding adjacent sides

Let's say adjacent sides are u,v.

u=P1P2鈬赌鈬�u=0i+2j+0kv=P1P3鈬赌鈬�v=-4i+3j+0k

03

Step 3. Finding the area

The crossproduct:

u脳v=ijk020-430u脳v=2030i-00-40j+02-43ku脳v=8k

04

Step 4. Finding the area

The area:

A=u脳vA=8kA=8

Therefore the area is8square units.

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