   Chapter 12.4, Problem 27E

Chapter
Section
Textbook Problem

# Find the area of the parallelogram with vertices A(−3, 0), B(−1, 3). C(5, 2), and D(3. −1).

To determine

To find: The area of the parallelogram with vertices A(3,0),B(1,3),C(5,2) and D(3,1) .

Explanation

Given:

A(3,0),B(1,3),C(5,2) and D(3,1) .

Formula:

Area of the parallelogram=|a×b| (1)

Here,

a and b are the vectors.

Write the expression for cross product between a and b .

a×b=|ijka1a2a3b1b2b3| (2)

From the vertices A(3,0),B(1,3),C(5,2) and D(3,1) draw the figure as shown in Figure 1.

Find AB .

AB=B(1,3)A(3,0)=[(1)(3)],(30)=(1+3),(30)=2,3

Consider the AB and AD as the three dimensional vectors are 2,3,0 and 6,1,0

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