Question 1 :
Direction cosines $l, m, n$ of two lines are connected by the equation $l-5m+3n=0$ and $7l^{2}+5m^{2}-3n^{2}=0$. The direction cosines of one of the lines are

Question 2 :
The straight line $\displaystyle \frac{x - 3}{3} = \frac{y - 2}{1} = \frac{z - 1}{0}$ is

Question 4 :
Direction cosines of ray from $P(1, -2, 4)$ to $Q(-1, 1, -2)$ are

Question 5 :
The product of the d.cs of the line which makesequal angles with $ox, oy, oz$ is<br>

Question 6 :
If the projection of a line segment on $x,y$ and $z$ axes are respectively $3,4$ and $5$, then the length of the line segment is

Question 7 :
The projection of the line segment joining $(0, 0, 0)$ and $(5, 2, 4)$ on the line whose direction ratios are $2, -3, 6$ is<br/>

Question 8 :
A lines makes angles $\dfrac{\alpha }{2},\dfrac{\beta }{2},\dfrac{\gamma }{2}$ with positive direction of coordinate axes, then $\cos \alpha&#160; + \cos \beta&#160; + \cos \gamma $ is equal to

Question 9 :
If $l,m,n$ are the d.cs of a line and $l=\displaystyle \dfrac{1}{3}$, then the maximum value of $l\times m\times n $ is<br/>

Question 10 :
The direction cosines of the line segment joining points $(-3, 1, 2)$ and $(1, 4, -10)$ is.

Question 11 :
Statement-1 &#160;: &#160;If a line makes acute angles $\alpha, \beta, \gamma, \delta$ with diagonals of a cube, then&#160;$ \displaystyle \cos^2\alpha+\cos^2\beta+\cos^2\gamma+\cos^2\delta=\frac{4}{3}$<br/>Statement 2 &#160;: &#160;If a line makes equal angle (acute) with the axes, then its direction cosine are $ \displaystyle&#160;\frac{1}{\sqrt{3}} , \frac{1}{\sqrt{2}}$ and $\dfrac{1}{\sqrt{3}}$

Question 12 :
If $A$ , $B$ and $C$ are three collinear points, where $A= i + 8 j - 5k $, $ B &#160;= 6i-2j$ and $C= 9i + 4j - 3 k$, then $B$ divides $AC$ in the ratio of :

Question 13 :
If $\alpha,\beta,\gamma\in[0,2\pi]$, then the sum of all possible values of $\alpha, \beta,\gamma$ if $\sin \alpha=-\dfrac{1}{\sqrt{2}}$, $\cos \beta=-\dfrac{1}{2}$, $\tan \gamma=-\sqrt{3}$, is

Question 15 :
If the points $a(cos \alpha + i sin \alpha)$ , $b(cos \beta + i sin \beta)$ and $c(cos \gamma + isin \gamma)$ are collinear then the value of $|z|$ is: <br>( where ${z = bc \ sin(\beta-\gamma) + ca \ sin(\gamma-\alpha) + ab \ sin(\alpha - \beta) + 3i -4k}$ )<br>

Question 16 :
If direction cosines of two lines are proportional to $(2,3,-6)$ and $(3,-4,5)$, then the acute angle between them is

Question 17 :
Assertion ($A$):&#160;Three points with position vectors $\vec{a},\vec{b},\ \vec{c}$ are collinear if $\vec{a}\times\vec{b}+\vec{b}\times\vec{c}+\vec{c}\times\vec{a}=\vec{0}$<br/><br/>Reason ($R$):Three points ${A}, {B},\ {C}$ are collinear if $\vec{AB}={t}\ \vec{BC}$, where ${t}$ is a scalar quantity.<br/>

Question 18 :
A line in the 3-dimensional space makes an angle $\theta \left(0 &lt; \theta \leq \dfrac {\pi}{2}\right)$ with both the x and y axes, then the set of all values of $\theta$ is the interval :

Question 19 :
The direction cosine of a line equally inclined to the axes are

Question 20 :
The direction ratios of the diagonal of a cube which joins the origin to the opposite corner are (when the three concurrent edges of the cube are coordinate axes)