List of top Mathematics Questions on Direction Cosines and Direction Ratios of a Line

The direction cosines $l,m,n$ of the two lines are connected by the relations $l+m+n=0$ and $lm=0$, then the angle between the lines is....

The position vector of a point $P$, such that $OP$ inclined to the X axis at $45^{\circ }$ and to the Y axis at $60^{\circ }$ and $|OP|=12$ units is:

If $l,m,n$ are direction cosines of a vector $\bar{r}$ such that $l+m+n=1$ and $l^{2}+m^{2}+n^{2}=1$, then:
(where $l,m,n\geq 0$)

If the line $\frac{x+4}{a}=\frac{y-2}{b}=\frac{z+1}{c}$ passes through the point $(-3,1,-2)$ and its direction is chosen such that it makes an acute angle $\gamma$ with the positive direction of Z- axis, then value of $\cos \gamma$ is:

If the direction cosines of the line $\frac{2x+5}{3}=\frac{2-3z}{-1};3y=-2$ are $\frac{9}{\sqrt{85}},m,\frac{2}{\sqrt{85}}$ then the value of $m$ is:

If the points $A(1,p,1),B(2,5,-1),C(q,11,r)$ are collinear. If the line passing through these points is perpendicular to the vector $4\hat{i}-2\hat{j}+\hat{k}$, then the value of $p+q+r$ is

A line makes the same angle $\alpha$ with each of the $X$ and $Z$ axes. If the angle $\beta$ which it makes with the $Y$-axis is such that $\sin ^{2}\beta =2\sin ^{2}\alpha$, then the value of $\cos ^{2}\alpha$ is ...

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

If $α,β,γ$ are the direction angles of the line $x = 4z+3$ and $y = 2-3z$, then the value of $cosα+cosβ+cosγ$ is...

The angle between a diagonal and one of its edges of a cube is ...................

If a unit vector makes angles $\frac{π}{4}$ with $\hat{i}$, $\frac{π}{3}$ with $\hat{j}$ and $θ\in (0,π)$ with $\hat{k}$, then a value of $θ$ is equal to...

The direction cosines of a line which is perpendicular to the lines $\frac{x-7}{2} = \frac{y+17}{-3} = \frac{z-6}{1}$ and $\frac{x+5}{1} = \frac{y+3}{2} = \frac{z-6}{-2}$ are...

The vector $\overset{̄}{r}$ whose magnitude is $3\sqrt{2}$ units and which makes angles of $\frac{π}{4}$ and $\frac{π}{2}$ with the positive y- and z-axes respectively is....

If a line makes angles $α,β,γ$ with the coordinate axes, then the sum of values of $sin^2α+sin^2β+sin^2γ$ and $cos2α+cos2β+cos2γ$ is ...

A vector $\overset{̄}{r}$ of magnitude $3\sqrt{2}$ units which makes angles of $\frac{π}{4}$ and $\frac{π}{2}$ respectively with Y and Z axes is

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

The angle between the lines whose direction cosines are $\frac{-\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}$ and $\frac{-\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}$ is

The angle between lines whose direction cosines satisfy the equation $l + m + n = 0$ and $l^2 - m^2 - n^2 = 0$, is ______.