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The position vectors of the vertices ...

The position vectors of the vertices of a quadrilateral with `A` as origin are `B( vec b),D( vec d)a n dC(l vec b+m vec d)dot` Prove that the area of the quadrialateral is `1/2(l+m)| vec bxx vec d|dot`

Text Solution

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Area of quandrilateral is `1/2|vec(AC)xxvec(BD)|=1/2|(lvecb+mvecd)xx(vecd-vecb)|`
`= 1/2 |lvecbxxvecd - mvecd xxvecb|`
`=1/2 ( l+m)|vecbxxvecd|`
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