Question

Lines $\overline{r}=(3+t)\hat{i}+(1-t)\hat{j}+(-2-2t)\hat{k}$, t$\in$R and x$=4+k$, $y=-k$, $z=-4-2k$, k$\in$R, then relation between lines is ___________.

• A. Skew
• B. Coincident
• C. Parallel
• D. Perpendicular

Answer 1

Answer: (C)

Parallel

For the first line,

$\overrightarrow{r}=(3+t)\hat{i}+(1-t)\hat{j}+(-2-2t)\hat{k}$

$=3\hat{i}+\hat{j}-2\hat{k}+t(\hat{i}-\hat{j}-2\hat{k})$

For the second line,

$\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}$

$=(4+k)\hat{i}+(-k)\hat{j}+(-4-2k)\hat{k}$

$=4\hat{i}-4\hat{k}+k(\hat{i}-\hat{j}-2\hat{k})$

It can be seen that the two lines have same direction ratios $(1,-1,-2)$.

Hence, the two lines are parallel.

So, the answer is option (C).