In triangle $OAB$, $C$ is the mid-point of $OA$. The point $D$ lies on $CB$ such that&nbsp

Question

In triangle $OAB$, $C$ is the mid-point of $OA$. The point $D$ lies on $CB$ such that $CD : DB = 2 : 3$. It is given that $\overrightarrow{OB} = \mathbf{b}$ and $\overrightarrow{OC} = \mathbf{c}$. The point $E$ lies on $AB$ such that $\overrightarrow{OE} = \lambda \overrightarrow{OD}$ and $\overrightarrow{AE} = \mu \overrightarrow{AB}$ where $\lambda$ and $\mu$ are real numbers. Express $\overrightarrow{OE}$ in terms of $\lambda$, $\mathbf{b}$ and $\mathbf{c}$. Express $\overrightarrow{OE}$ in terms of $\mu$, $\mathbf{b}$ and $\mathbf{c}$. Hence, find the values of $\lambda$ and $\mu$.

Accepted Answer

(a) $\frac{2\lambda }{5}\mathbf{b}+\frac{3\lambda }{5}\mathbf{c}$ (b) $\mu \mathbf{b}+\left( 2+2\mu \right)\mathbf{c}$ (c) $\lambda =\frac{10}{7},\,\,\mu =\frac{4}{7}$

Vectors - Vector Algebra

Vectors - Vector Algebra