Question

The following lines are $\hat{r}=(\hat{i}+\hat{j})+\lambda (\hat{i}+2\hat{j}-\hat{k})+\mu (-\hat{i}+\hat{j}-\widehat{2k})$

• A. collinear
• B. skew-lines
• C. co-planar lines
• D. parallel lines

Answer 1

Answer: (A)

collinear

Condition for three lines $\overrightarrow{r_1}$ , $\overrightarrow{r_2}$ , and $\overrightarrow{r_3}$ to be collinear is:

$\overrightarrow{r_1}+\lambda \overrightarrow{r_2}+\overrightarrow{{\mu r}_3}=0$

where $\overrightarrow{r_1}=(\overrightarrow{i}+\overrightarrow{j})$

$\overrightarrow{r_2}=(\overrightarrow{i}+2\overrightarrow{j}-\overrightarrow{k})$

$\overrightarrow{r_3}=(-\overrightarrow{i}+\overrightarrow{j}-2\overrightarrow{k})$

and $\lambda$ and $\mu$ are scalars

Hence, the answer is collinear.