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Diagonals of a parallelogram are respre...

Diagonals of a parallelogram are respresented by vectors `vecA = 5hati - 4hatj + 3hatk and vecB = 3hati +2hatj - hatk`. Area of the parallelogram is :

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When `vecAandvecB` are the diagonals of a parallelogram, then its
Area `=(1)/(2)|vecAxxvecB|vecAxxvecB=|(hati,hatj,hatk),(5,-4,3),(3,-2,1)|=i|(-4,3),(-2,-1)|-j|(5,3),(3,-1)|+k|(5,-4),(3,-2)|`
`=hati{(-4)(-1)-(3)(-2)}-hatj{(5)(-1)-(3)(3)}+hatk{5)(-2)-(-4)(3)}=10hati+14hatj+2hatk`
`|vecAxxvecB|=sqrt((10)^(2)+(14)^(2)+(2)^2)=sqrt(300)` area of parallelogram `(1)/(2)|vecAxxvecB|(1)/(2)xx10sqrt(3)=5sqrt(3)`
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