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Chapter 9: Q. 48 (page 627)

In Problem, find the area of the parallelogram with one corner at P1 and adjacent sides

P1P2鈫�andP1P3鈫�

P1=-2,0,2,P2=2,1,-1,P3=2,-1,2

Short Answer

Expert verified

The area of the parallelogram is :217

Step by step solution

01

Step1.Giving information 

three pointsP1-2,0,2,P22,1,-1,P32,-1,2

We know that the vector is formed by two points like

A=x2-x1i+y2-y1j+z2-z1k

To given question

U=P1P2鈫�U=(2-(-2))i+1-0j+-1-2kU=4i+j-3klikethatv=4i-j

02

Step2. calculation cross product of vectors 

We know that to find the area of a parallelogram by two vectors. it's necessary to find an orthogonal vector, for that

u脳v=ijk41-34-10u脳v=i1-3-10-j4-340+k414-1u脳v=-3i-12j-8k

03

Step3. calculations of area 

area of the parallelogram is :u脳v

u脳v=-3i-12j-8ku脳v=9+144=64u脳v=217

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Most popular questions from this chapter

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