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Two sides of a parallelogram are given as 1 + 2j - 3k and 5i+j-k. Find area of parallelogram and also find the area of triangle formed by the diagonal of the parallelogram.​

103. B.

53. C.

53. The area of a parallelogram is given by 21× the cross product of its diagonals. So, area =21[(3i^+j^−2k^)×(i^−3j^+4k^)] =21∣∣∣∣∣∣∣∣i^31j^1−3k^−24∣∣∣∣∣∣∣∣ =21∣∣∣∣i^(4−6)−j^(12+2)+k^(−9−1)∣∣∣∣ =21∣∣∣∣(−2i^−14j^−10k^)∣∣∣∣ =1+49+25. =75. Answer verified by Toppr. Practice important Questions. Algebra 1. 2988 Qs.

i think the answer is a and b

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