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Chapter 9: Q. 25 (page 632)

Find the area of the parallelogram that has uand v as adjacent sides.

Short Answer

Expert verified

The area of the parallelogram is115

Step by step solution

01

Step 1.  Given information is 

u=2j-3j+kv=-i+3j+2k

02

Step 2. If u=a1i+b1j+c1k, v=a2i+b2j+c2k are two vectors, then cross product isu×v=(b1c2-b2c1)i-(a1c2-a2c1)j-(a1b2-a2b1)k

We have a1=2,b1=-3,c1=1,a2=-1,b2=3,c2=2

u脳v=(-3脳2-3脳1)i-(2脳2-(-1)脳1)j-(2脳3-(-1)(-3))ku脳v=(-9)i-(5)j+3ku脳v=-9i-5j+3k

03

Step 3. Area of a parallelogram is A=u×v

=(-9)2+(5)2+(3)2=81+25+3=115

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Most popular questions from this chapter

In Problems 39鈥�54, the polar coordinates of a point are given. Find the rectangular coordinates of each point.

8.1,5.2

In Problems 47鈥�52, find the unit vector in the same direction asv:v=i-jv=i-j

Findzwand zw. Leave the answers in polar form.

role="math" localid="1646661399572" z=2+2iw=3-i

find the unit vector in the same direction asv

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Plot the point whose rectangular coordinates are (3,-1).

What quadrant does the point lie in?
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