K. C. Sinha and Abhishek Chandra Solutions for Exercise 1: EXERCISE

If a line makes angles ${90}^{°}, {135}^{°}, {45}^{°}$ with the $x, y$ and $z$-axes respectively, find its direction cosines.

If $\begin{array}{l}\overrightarrow{r}=2\hat{i}-3\hat{j}+2\hat{k}\end{array},$ find the direction cosines of  $\overrightarrow{r}$.

If a line has direction ratios $-18, -12, -4,$ then what are its direction cosines?

Find the direction cosines of the sides of the triangle whose vertices are $\left(3,5,-4\right), \left(-1,1,2\right)$ and $\left(-5,-5,-2\right)$

Find the angles of $∆ABC$ whose vertices are $A\left(-1,3,2\right), B\left(2,3,5\right)$ and $C\left(3,5,-2\right)$.

Find the angle between the lines whose direction cosines are given by the equations $l+2m+3n=0$ and $3lm-4ln+mn=0$.

Find the projection of the line segment joining $\left(2,-1,3\right)$ and $\left(4,2,5\right)$ on a line which makes equal acute angles with coordinate axes.

The projection of a directed line segment on the coordinate axes are $12, 4, 3$. Find its length and direction cosines.