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Calculate the area of the parallelogram ...

Calculate the area of the parallelogram when adjacent sides are given by the vectors `vec(A)=hat(i)+2hat(j)+3hat(k)` and `vec(B)=2hat(i)-3hat(j)+hat(k)`.

Text Solution

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We know that area of the parallelogram is equal to magnitude of the cross product of given vectors.,Now
`vec(A)xxvec(B)=|(hat(i), hat(j), hat(k)) ,(1,2,3), (2 ,-3 ,1)|`
`=hat(i)(2+9)+hat(j)(6-1)+hat(k)(-3-4)=11hat(i)+5hat(j)-7hat(k)`
So area of parallelogram: `|vec(A)xxvec(B)|=sqrt(11^(2)+5^(2)+(-7)^(2))`
`=sqrt(195)sq.unit`
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