The position vectors of the points $X$, $Y$ and $Z$, relative to an origin are $3\mathbf{m}$

Question

The position vectors of the points $X$, $Y$ and $Z$, relative to an origin are $3\mathbf{m}$, $2\mathbf{n}$ and $\frac{1}{2}\mathbf{m}-\mathbf{n}$ respectively. Given that $\overrightarrow{XY} = \lambda \overrightarrow{XP}$ and $\overrightarrow{OZ} = \mu \overrightarrow{OP}$, where $\lambda$ and $\mu$ are non-zero constants, express $\overrightarrow{OP}$ in terms of $m$, $n$ and $\lambda$, express $\overrightarrow{OP}$ in terms of $m$, $n$ and $\mu$, hence, evaluate $\lambda$ and $\mu$.

Accepted Answer

(i) $\vec{OP}=\frac{2}{\lambda}\mathbf n+\left(3-\frac{3}{\lambda}\right)\mathbf m$; (ii) $\vec{OP}=\frac{1}{\mu}\left(\frac12\mathbf m-\mathbf n\right)$; (iii) $\lambda=\frac23$, $\mu=-\frac13$.

Vectors - Vector Algebra

Vectors - Vector Algebra

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