List of top Mathematics Questions on Direction Cosines and Direction Ratios of a Line asked in CBSE CLASS XII

Direction ratios of lines $l_1$ and $l_2$ respectively are $\langle 1, 0, 0\rangle$ and $\langle 0, -1, 0\rangle$. The direction ratios of the line perpendicular to both $l_1$ and $l_2$ are :

Direction cosines of the line given by equations : $\frac{2x-1}{4} = \frac{1-y}{3} = \frac{-z}{6}$ are

A unit vector $\vec{a}$ is such that it makes an angle $\frac{\pi}{4}$ with the $x$-axis, $\frac{\pi}{3}$ with the $y$-axis and an acute angle $\theta$ with the $z$-axis. Find $\theta$ and the components of $\vec{a}$.

If $ l_1, m_1, n_1 $ and $ l_2, m_2, n_2 $ are direction cosines of lines $ L_1 $ and $ L_2 $ respectively and $ \theta $ is the acute angle between them, then :

Direction ratios of lines $ l_1 $ and $ l_2 $ respectively are $ \langle 1, -2, 3 \rangle $ and $ \langle -2, p, -6 \rangle $. The value of p for which $ l_1 \parallel l_2 $, is :

Assertion (A): A line can have direction cosines $\langle 1, 1, 1 \rangle$.
Reason (R): $\cos\theta = 1$ is possible for $\theta = 0$.

The direction cosines of the line given by $x = y = 1 - z$ are:

Assertion (A): A line can have direction cosines $\langle 1,1,1\rangle$.
Reason (R): $\cos\theta=1$ is possible for $\theta=0^\circ$.

Direction cosines of line $x=y=1-z$ are

If the direction cosines of a line are $\lambda, \lambda, \lambda$, then $\lambda$ is equal to: