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The diagonals of a parallelogram are expressed as `vecA=5hati05hatj+3hatk` and `hatB=3hatj-2hatj-hatk`. Calculate the magnitude of area of this parallelogram. |
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Answer» When `vecA` and `vecB` are the diagonals of a parallelegram, 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)(-2)-(-4)(3)}=10hati+14hatj+2hatk` therefore `|vecAxxvacB|=sqrt((10)^(2)+(14)^(2)+(2)^(2))=sqrt(300)` So area of parallelogram `=(1)/(2)|vecAxxvecB|=(1)/(2)xx10sqrt(3)=5sqrt(3)` |
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