Let A ( 2 , 3 , 5 ) and C ( - 3 , 4 , - 2 ) be opposite vertices of a parallelogram A B C D if the diagonal B D → = i ^ + 2 j ^ + 3 k ^ then the area of the parallelogram is equal to

Question

Let A ( 2 , 3 , 5 ) and C ( - 3 , 4 , - 2 ) be opposite vertices of a parallelogram A B C D if the diagonal B D → = i ^ + 2 j ^ + 3 k ^ then the area of the parallelogram is equal to, 1 2 410, 1 2 474, 1 2 586, 1 2 306

MARKS App · Accepted Answer

Area of the parallelogram is given by 1 2 A C → × B D → . ⇒ Area = 1 2 - 5 i ^ + j ^ - 7 k ^ × i ^ + 2 j ^ + 3 k ^ ⇒ Area = 1 2 i ^ j ^ k ^ - 5 1 - 7 1 2 3 ⇒ Area = 1 2 17 i ^ + 8 j ^ - 11 k ^ ⇒ Area = 1 2 289 + 64 + 121 ⇒ Area = 474 2 square units.

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