Chapter 11.4, Problem 25E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Area In Exercises 25 and 26, find the area of the triangle with the given vertices. (Hint: 1 2 ‖ u × v ‖ is the area of the triangle having u and v as adjacent sides.) A ( 0 , 0 , 0 ) , B ( 1 , 0 , 3 ) , C ( − 3 , 2 , 0 )

To determine

To calculate: Area of triangle with vertices A(0,0,0),B(1,0,3),C(3,2,0).

Explanation

Given:

The vertices of triangle are:A(0,0,0),B(1,0,3),C(âˆ’3,2,0).

Formula used:

The area of triangle is given by:A=12â€–uÃ—vâ€–.

Calculation:

Area of triangle having u and v as adjacent sides is given by below formula:

A=12â€–uÃ—vâ€–

ABâ‡€=i+0j+3k=<1,0,3>

ACâ‡€=âˆ’3i+2j+0k=<âˆ’3,2,0>

ABâ‡€Ã—ACâ‡€=|ijk103âˆ’320|=i(0

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