Question

If $P\left(\overrightarrow{p}\right),Q\left(\overrightarrow{q}\right),R\left(\overrightarrow{r}\right)$ and $S\left(\overrightarrow{s}\right)$ 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. Parallel
• C. Intersecting
• D. None of these

Answer 1

The correct option is C Intersecting

here from eq

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

if we let $p=q=r=s=\hat{i}+\hat{j}+\hat{k}$

i.e. points are equal

Line PQ$\overrightarrow{r}=\hat{i}+\hat{j}+\hat{k}$

Line RS$\overrightarrow{r}=\hat{i}+\hat{j}+\hat{k}$

it is intersecting becuase if the any point vector of two lines is same then they intersect at that point and here it is true