Question

Which of the following is true for lines $\overrightarrow{r_1}=(\hat{i}+2\hat{j}-3\hat{k})+s(3\hat{i}+\hat{j}-\hat{k})$ and $\overrightarrow{r_2}=(4\hat{i}+\hat{j}-\hat{k})+t(2\hat{i}-\hat{j}+3\hat{k})$.

• A. Do not intersect
• B. Intersect
• C. Perpendicular to each other
• D. Can not be determined

Answer 1

Answer: (A)

Do not intersect

$\overrightarrow{r_1}=(\hat{i}+2\hat{j}-3\hat{k})+s(3\hat{i}+\hat{j}-\hat{k})$

$\overrightarrow{r_2}=(4\hat{i}+\hat{j}-\hat{k})+t(2\hat{i}-\hat{j}+3\hat{k})$

$\overrightarrow{r_1}=(3s+1)\hat{i}+(s+2)\hat{j}-(s+3)\hat{k}$

$\overrightarrow{r_2}=(2t+4)\hat{i}+(-t+1)\hat{j}+(3t-1)\hat{k}$

For number value of s and t

$\frac{1+3S}{4+2t}=\frac{2+s}{1-t}=\frac{-(3+s)}{3t-1}$

They do not intersect.

Hence option A is correct.