Q92 / 200 · Manipal (MET) 2010 · Mathematics
If $P(\overrightarrow{\mathrm{p}}), Q(\overrightarrow{\mathrm{q}}), R(\overrightarrow{\mathrm{r}})$ and $S(\overrightarrow{\mathrm{~s}})$ be four points such that $3 \vec{p}+8 \vec{q}=6 \vec{r}+5 \vec{s}$, then the lines $P Q$ and $R S$ are
- Askew
- Correct answerBintersecting
- Cparallel
- DNone of these
Solution
Given, $3 \overrightarrow{\mathbf{p}}+8 \overrightarrow{\mathbf{q}}=6 \overrightarrow{\mathbf{r}}+5 \vec{s}$
$\Rightarrow \frac{3 \vec{p}+8 \vec{q}}{8+3}=\frac{6 \overrightarrow{\mathrm{r}}+5 \overrightarrow{\mathrm{~s}}}{6+5}$
$\Rightarrow$ The point which divides $P Q$ in ratio $8: 3$ in the same as the point which divides $R S$ in the ratio $5: 6$. Hence, the line $P Q$ and $R S$ intersect.
Hence, the correct answer is option: 'B'.