Question

For the given statements,
Statement $1$: Links $\overrightarrow{r}=\hat{i}-\hat{j}+\lambda (\hat{i}+\hat{j}-\hat{k})\text{and}\overrightarrow{r}=2\hat{i}-\hat{j}+\mu (\hat{i}+\hat{j}-\hat{k})$ do not intersect.
Statement $2$: Skew lines never intersect.
Which of the following is correct:

• A. Both the statements are true, and Statement $2$ is the correct explanation for statement $1$.
• B. Both satements are true, but statement $2$ is not the correct explanation for statement $1$.
• C. Statement $1$ is true and statement $2$ is false
• D. Statement $1$ is false and statement $2$ is true

Answer 1

The correct option is B Both satements are true, but statement $2$ is not the correct explanation for statement $1$.

Given lines are parallel as both are directed along the same vector $(\hat{i}+\hat{j}-\hat{k});$ also they passes through $A(1,-1,0),B(2,-1,0)$ respectively.
D.R's of $AB=(1,0,0)\ne (1,1,-1).$
So given lines are parallel not collinear.So they do not intersect Also statement $2$ is correct by defination of skew lines, but skew lines are those which are neither parallel nor intersecting. Hence, both the statements are true, but statement $2$ is not the correct explanation for statement $1$.