Question

If P($\overrightarrow{p}$), Q($\overrightarrow{q}$), R($\overrightarrow{r}$) and S($\overrightarrow{s}$) be four points such that

3$\overrightarrow{p}$ + 8$\overrightarrow{q}$ = 6$\overrightarrow{r}$ + 5$\overrightarrow{s}$, then the lines PQ and RS are –

• A. skew
• B. intersecting
• C. parallel
• D. none of these

Answer 1

Answer: (B)

intersecting

Answer 2

Given 3$\overrightarrow{p}$ + 8$\overrightarrow{q}$ = 6$\overrightarrow{r}$ + 5$\overrightarrow{s}$

Ž $\frac{3\overrightarrow{p} + 8\overrightarrow{q}}{8 + 3}$ = $\frac{6\overrightarrow{r} + 5\overrightarrow{s}}{5 + 6}$

Ž The point which divides PQ in ratio 8 : 3 is the same as the point which divides RS in the ratio 5 : 6.

Hence, the line PQ and RS intersect.