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If a parallelogram ABCD, |AB|=a, |AD|=b and |AC|=C, then DA. AB is equal to |
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Answer» `(1)/(2)(a^(2)+b^(2)+c^(2))` In `Delta ABC,""AB + BC = AC ` `rArr AB+AD=AC "" [ because BC=AD]` `rArr AB-DA=AC "" [ because AD=-DA]` `rArr |AB-DA|=|AC|` `rArr |AB-DA|^(2)=|AC|^(2)` `rArr |AB|^(2)+|DA|^(2)-2AB*DA=(AC)^(2)` `rArr a^(2)+b^(2)-2AB*DA=c^(2) "" [ because |AD|=|DA|=b]` `rArr 2DA *AB=a^(2)+b^(2)-c^(2)` `rArr DA*AB=(1)/(2)[a^(2)+b^(2)-c^(2)]` |
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