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InterviewSolution
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The area of the parallelogram whose diagonals are the vectors `hati+3hatj- 2hatk and 3hati+hatj-4hatk`A. `3sqrt(42)` sq unitsB. `sqrt(42)` sq untisC. `2sqrt(42)` sq unitsD. None of these |
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Answer» Correct Answer - A Let `a=hat(i)+3hat(j)-2hat(k) and b=3hat(i)+hat(j)-4hat(k)` The `a xxb=|{:(hat(i),hat(j),hat(k)),(1,3,-2),(3,1,-4):}|` `=hat(i)(-12+2)-hat(j)(-4+6)+hat(k)(1-9)` `=-10hat(i)-2hat(j)-8hat(k)` `therefore` Area of parallelogram `=(1)/(2)|axxb|` `=(1)/(2)sqrt((-10)^2+(-2)^2+(-8)^2)` `=(1)/(2)sqrt(100+4+64)=(1)/(2)sqrt(168)` `=sqrt(42)` sq.units. |
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