InterviewSolution
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InterviewSolution
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Consider a parallelogram whose vertices are A (1, 2), B (4, y), C (x, 6) and D (3, 5) taken in order. What is the area of the parallelogram ?A. `7/2` square unitsB. 4 square unitsC. `11/2` square unitsD. 7 square units |
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Answer» Correct Answer - D Area of parallelogram `=2` area of `Delta ADB` `vec(a)=vec(AB)=(4-1) hat(i)+(3-2)hat(j)` `vec(b)=vec(AB)=(3-1) hat(i)+(5-2) hat(j)` `:.` Area of parallelogram `=2[1/2| vec(a)xxvec(b)|]=|vec(a)xxvec(b)|` Now, `vec(a)xxvec(b)=|(hat(i),hat(j),hat(k)),(3,1,0),(2,3,0)|=7 hat(k)` `:.` Area `=|vec(a)xxvec(b)|=|7hat(k)|=sqrt(49)=7` square unit |
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