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)`.

Calculate the area of the parallelogram when adjacent sides are given

1.	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)`.
Answer» 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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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)`.

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