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प्रश्न
Using vectors, prove that the parallelogram on the same base and between the same parallels are equal in area.
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उत्तर
Let ABCD and ABFE be two parallelograms on the same base AB and between same parallel lines AB and DF.
Let `vec"AB" = vec"a"` and `vec"AD" = vec"b"`
∴ Area of parallelogram ABCD = `|vec"a" xx vec"b"|`
= `|vec"a" xx (vec"AD" + vec"DE")|`
= `|vec"a" xx (vec"b" xx "K"vec"a")|`
= `|(vec"a" xx vec"b") + "K"(vec"a" xx vec"a")`
= `|vec"a" xx vec"b"| + 0` ...`["becuase" vec"a" xx vec"a" = 0]`
= `|vec"a" xx vec"b"|`
Hence proved.
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