R D Sharma Solutions for Chapter: Directions Cosines and Direction Ratios, Exercise 2: VERY SHORT ANSWER QUESTIONS (VSAQs)

A line makes an angle of $60°$ with each of $x$-axis and $y$-axis. Find the acute angle made by the line with $z$-axis.

Write the ratio in which the line segment joining $(a, b, c)$ and $(-a, -c, -b)$ is divided by the $XY$-plane.

Write the inclination of a line with $Z$-axis, if its direction ratios are proportional to $0, 1, -1$.

Write the angle between the lines whose direction ratios are proportional to $1, -2, 1$ and $4, 3, 2$.

Write the distance of the point $P(x, y, z)$ from $XOY$ plane.

Find the distance of the point $(2, 3, 4)$ from the $x$-axis.

If a unit vector $\overrightarrow{a}$ makes an angle $\frac{\pi }{3}$ with $\hat{i}, \frac{\pi }{4}$ with $\hat{j}$ and an acute angle $\theta$ with $\hat{k}$, then find the value of $\theta$.

Write the distance of a point $P(a, b, c)$ from $x$-axis.