Relative to the origin $O$, the position vectors of $A$, $B$ and $C$ are $\mathbf{a}$, \(\

Question

Relative to the origin $O$, the position vectors of $A$, $B$ and $C$ are $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{c}$ respectively where $\mathbf{c}=3\mathbf{a}-5\mathbf{b}$. Given that $\left| \mathbf{a} \right|=\sqrt{6}$, $\mathbf{b}$ is a unit vector and the angle between $\mathbf{a}$ and $\mathbf{b}$ is $\frac{2}{3}\pi $, find the exact area of triangle $ABC$.

Accepted Answer

$\dfrac{9\sqrt2}{4}$ square units

Vectors - Areas of Triangles and Parallelograms Using Vectors

Vectors - Areas of Triangles and Parallelograms Using Vectors

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