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Chapter 9: Q. 49 (page 627)

In Problem, find the area of the parallelogram with vertices P1, P2, P3, and P4

P1=1,1,2,P2=1,2,3,P3=-2,3,0,P4=-2,4,1

Short Answer

Expert verified

The area of the parallelogram is :34

Step by step solution

01

Step1. Given information 

four pointsP1=1,1,2,P2=1,2,3,P3=-2,3,0,P4=-2,4,1

We know that the vector is formed by two points like

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

To given question

U=P1P2鈫�V=P1P3鈫�U=1-1i+2-1j+3-2kU=j+klikethatV=-3i+2j-2k

02

Step2. Calculating the orthogonal vector of u and v 

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

U=j+kV=-3i+2j-2ku脳v=ijk011-32-2u脳v=i112-2-j01-3-2+k01-32u脳v=-4i-3j+3k

03

Step3. Calculating the resultant of orthogonal vector 

u脳v=-4i-3j+3ku脳v=16+9+9u脳v=34

resultant of orthogonal vector = area of given parallelogram

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