R D Sharma Solutions for Chapter: Straight Line in Space, Exercise 1: EXERCISE

Find the vector and cartesian equations of the line through the point $(5, 2, -4)$ and which is parallel to the vector $3\hat{i}+2\hat{j}-8\hat{k}.$

Find the vector equation of a line which is parallel to the vector $2\hat{i}-\hat{j}+3\hat{k}$ and which passes through the point $(5, -2, 4)$. Also, reduce it to cartesian form.

Find the vector equation for the line which passes through the point $(1,2,3)$ and parallel to the vector $\hat{i}-2\hat{j}+3\hat{k}$. Reduce the corresponding equation in cartesian from.

The cartesian equations of a line are $\frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}$. Find a vector equation for the line.

Find the direction cosines of the line $\frac{4-x}{2}=\frac{y}{6}=\frac{1-z}{3}.$ Also, reduce it to vector form.

The cartesian equations of a line are $x=a y+b, z=c y+d$ Find its direction ratios and reduce it to vector form.

Show that the points whose position vectors are $-2\hat{i}+3\hat{j},\hat{i}+2\hat{j}+3\hat{k}$ and $7\hat{i}+9\hat{k}$ are collinear.

Find the cartesian and vector equations of a line which passes through the point $(1, 2, 3)$ and is parallel to the line $\frac{-x-2}{1}=\frac{y+3}{7}=\frac{2z-6}{3}.$