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) $\dfrac{2\lambda}{5}\mathbf b+\dfrac{3\lambda}{5}\mathbf c$ (b) $\mu\mathbf b+(2-2\mu)\mathbf c$ (c) $\lambda=\dfrac{10}{7},\;\mu=\dfrac47$.

Vectors - Vector Algebra

Vectors - Vector Algebra

Solution:

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