If diagonals of a parallelogram are (i-j) and (i+j). then area of the parallelogram will be (1) 0.5 unit (3) 2 unit (2) 1 unit (4) 4 unit
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We know the magnitude of area of a parallelogram made by the vectors and as the adjacent sides is,
Let and be the diagonal vectors of the parallelogram. Then,
On adding (2) and (3),
And on subtracting (3) from (2),
Hence (1) becomes,
Since for any arbitrary vector
Since
Or,
Here,
Then,
Since and
Hence the answer is 1 unit.
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