Practicing Success
Practicing Success
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In a parallelogram ABCD, $|\vec{AB}|=a,\,|\vec{AD}|=b$ and $|\vec{AC}|=c$, then $\vec{DB}.\vec{AB}$ has the value: |
$\frac{3a^2+b^2-c^2}{2}$ $\frac{a^2+3b^2-c^2}{2}$ $\frac{a^2-b^2+3c^2}{2}$ $\frac{a^2+3b^2+c^2}{2}$ |
$\frac{3a^2+b^2-c^2}{2}$ |
$\vec{DB}.\vec{AB}=(\vec{AB}-\vec{AD}).(\vec{AB})=|\vec{AB}|^2-\vec{AD}.\vec{AB}$ $=a^2-ab\cosθ=a^2+ab[\frac{b^2+a^2-c^2}{2ab}]=\frac{2a^2+b^2+a^2-c^2}{2}=\frac{3a^2+b^2-c^2}{2}$ |
