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प्रश्न
Using vectors, prove that the parallelogram on the same base and between the same parallels are equal in area.
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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