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Chapter 9: Q. 46 (page 559)

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

P1P2鈫�andP1P3鈫�

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

Short Answer

Expert verified

The area of the parallelogram is 213

Step by step solution

01

Step1. Given equation 

three pointsP1=0,0,0,P2=2,3,1,P3=-2,4,1

We know that the vector is formed by two points like

To given question

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

02

Step2. Calculation of cross product 

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=ijk231-241u脳v=i3242+j21-21+k23-24u脳v=-i-4j+14k

03

Step3.Calculation of area 

The area of parallelogram = u脳v

u脳v=-i-4j+14ku脳v=1+16+196u脳v=213

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