R D Sharma Solutions for Chapter: Straight Line in Space, Exercise 6: VERY SHORT ANSWER QUESTIONS (VSAQs)

Cartesian equations of a line $AB$ are $\frac{2x-1}{2}=\frac{4-y}{7}=\frac{z+1}{2}$. Write the direction cosines of a line parallel to $AB$.

Write the direction cosines of the line whose cartesian equations are $2x=3y=-z$

Write the angle between the lines $2x=3y=-z$ and $6x=-y=-4z.$

Write the condition for the lines $\overrightarrow{r}=\overrightarrow{a_1}+\lambda \overrightarrow{b_1}$ and $\overrightarrow{r}=\overrightarrow{a_2}+\mu \overrightarrow{b_2}$ to be intersecting.

The cartesian equations of a line $AB$ are $\frac{2x-1}{\sqrt{3}}=\frac{y+2}{2}=\frac{z-3}{3}$ Find the direction cosines of a line parallel to $AB.$

Find the Cartesian equations of the line which passes through the point $(-2, 4 , -5)$ and is parallel to the line $\frac{x+3}{3}=\frac{4-y}{5}=\frac{z+8}{6}.$

Find the angle between the lines $\overrightarrow{r}=\left(2\hat{i}-5\hat{j}+\hat{k}\right)+\lambda \left(3\hat{i}+2\hat{j}+6\hat{k}\right)$ and $\overrightarrow{r}=7\hat{i}-6\hat{k}+\mu \left(\hat{i}+2\hat{j}+2\hat{k}\right)$

Find the angle between the lines $2x=3y=-z$ and $6x=-y=-4z$