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प्रश्न
If `vec"a"` and `vec"b"` represent a side and a diagonal of a parallelogram, find the other sides and the other diagonal
उत्तर
Let ABCD be a parallelogram
Let `vec"AB" = vec"a"`
`vec"AC" = vec"b"`
Since ABCD is a parallelogram , we have
`vec"AB" = vec"DC"` and `vec"BC" = vec"AD"`
In triangle ABC, by triangle law
`vec"AB" + vec"BC" = vec"AC"`
`vec"BC" = vec"AC" - vec"AB"`
`vec"BC" = vec"b" - vec"a"`
∴ `vec"AD" = vec"b" - vec"a"`
`vec"DA" + vec"AB" = vec"DB"`
`- vec"AD" + vec"AB" = vec"DB"`
`-(vec"b" - vec"a") + vec"a" = vec"DB"`
`-vec"b" + vec"a" + vec"a" = vec"DB"`
`2vec"a" - vec"b" = vec"DB"`
The sides are `vec"AB" = vec"a", vec"BC" =vec"b" - vec"a"`
`vec"DC" = vec"a", vec"AD" =vec"b" - vec"a"`
Diagnals are `vec"AC" = vec"b", vec"DB" = 2vec"a" - vec"b"`
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