Question

Find the area of the parallelogram whose diagonals are represented by 3î +3 +and î-j-k 1) 252 2) va 3) 312 4) 512​

Answer 1

Answer:

Given diagonals are, AC=3i^+j^−2k^, DB=i^−3j^+4k^  

therefore, AB=AO+OB=2AC+2DB=21(3i^+j^−2k^)+21(i^−3j^+4k^)=2i^−j^+k^  

AC×AB=(3i^+j^−2k^)×(2i^−j^+k^)=−i^−7j^−5k^

thus,  the area of a parallelogram=∣AC×AB∣=12+72+52=75=53unit

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