Question 1 :
The direction cosines of a line which is equally inclined to axes, is given by

Question 2 :
A vector is equally inclined to the $x$-axis, $y$-axis and $z$-axis respectively, its direction cosines are

Question 3 :
Direction cosines of ray from $P(1, -2, 4)$ to $Q(-1, 1, -2)$ are

Question 4 :
A line passes through the points $(6, -7, -1)$ and $(2, -3, 1)$. The direction cosines of the line so directed that the angle made by it with the positive direction of x-axis is acute, is?

Question 5 :
What are the DR's of vector parallel to $\left( 2,-1,1 \right) $ and $\left( 3,4,-1 \right) $?

Question 6 :
<span>From the point $P(3, -1, 11)$, a perpendicular is drawn on the line $L$ given by the equation $\dfrac {x}{2} = \dfrac {y - 2}{3} = \dfrac {z - 3}{4}$. Let $Q$ be the foot of the perpendicular.</span><div>What are the direction ratios of the line segment $PQ$?</div>

Question 7 :
Can $\dfrac{1}{\sqrt{3}}, \dfrac{2}{\sqrt{3}}, \dfrac{-2}{\sqrt{3}}$ be the direction cosines of any directed line?

Question 8 :
If the dr's the line are $(1+\lambda, 1-\lambda, 2)$ and it makes an angle ${60}^{o}$ with the Y-axis then $\lambda$ is

Question 9 :
If a line makes the angles $ \alpha&#160;, \beta$ and $\gamma$ with the axes, then what is the value of $1+\cos 2\alpha +\cos 2\beta+\cos 2\gamma$<span>&#160;equal to ?</span>

Question 11 :
$l = m =n = 1$ represents the direction cosines of&#160;<br/><br/>

Question 12 :
The projections of a directed line segment on the coordinate axes are $12, 4, 3$ respectively.<div>What are the direction cosines of the line segment?</div>

Question 13 :
The direction cosines of the vectors $2\vec {i} + \vec {j} - 2\vec {k}$ is equal to

Question 14 :
The direction ratios of the diagonal of the cube&#160;joining the origin to the opposite corner are&#160;(when the $3$ concurrent edges of the cube are&#160;coordinate axes)<br/>

Question 15 :
Cosine of the angle between two diagonals of a&nbsp;cube is equal to

Question 16 :
If $P(x, y, z)$ moves such that $x=0, z=0$, then the&#160;locus of $P$ is the line whose d.cs are<br/>

Question 17 :
<table class="table table-bordered"><tbody><tr><td>&#160;List I</td><td>List II&#160;</td></tr><tr><td><span>1) d.c's of $x -$ axis</span></td><td><span>a) $(1,1,1)$</span>&#160;</td></tr><tr><td><span>2) d.c's of $y -$ axis</span></td><td><span>b)$\left(\displaystyle \frac{]}{\sqrt{3}}\frac{]}{\sqrt{3}},\frac{]}{\sqrt{3}}\right)$</span></td></tr><tr><td><span>3) d.c's of $z -$ axis</span></td><td><span>c) $(1,0,0)$</span><br/></td></tr><tr><td><span>4) d.c's of a line makes&#160;</span><span>equal angles with axes</span></td><td><span>d) $(0,1,0)$</span></td></tr><tr><td>&#160;</td><td><span>e) $(0,0,1)$</span></td></tr></tbody></table>The correct order for 1, 2, 3, 4 is

Question 18 :
Direction cosines of the line $\cfrac { x+2 }{ 2 } =\cfrac { 2y-5 }{ 3 } ,z=-1$ are ____

Question 19 :
The projection of the join of the two points $(1,4,5), (6,7,2)$ on the line whose d.s's are $(4,5,6)$ is

Question 20 :
lf the projections ofthe line segment${A}{B}$ on the $yz$-plane, $zx$-plane, $xy$-plane are $\sqrt{160}, \sqrt{153},5$ respectively, then the projection of ${A}{B}$ on the ${z}$-axis is<br/>

Question 21 :
If the d.rs of $OA$ and $OB$ are $1, -1, -1$ and $2, -1, 1$,&#160;then the d.cs of the line perpendicular to both $OA$&#160;and $OB$ are<br/>

Question 22 :
A line $AB$ in three-dimensional space makes angles $45^{\mathrm{o}}$ and $120^{\mathrm{o}}$ with the positive $\mathrm{x}$-axis and the positive $\mathrm{y}$-axis respectively. lf $AB$ makes an acute angle $e$ with the positive $\mathrm{z}$-axis, then $e$ equals <br>

Question 23 :
Direction ratio of line given by $\dfrac { x-1 }{ 3 } =\dfrac { 6-2y }{ 10 } =\dfrac { 1-z }{ -7 } $ are:

Question 25 :
If $l, m, n$ are the d.cs of the line joining $(5, -3, 8)$&#160;and $(6, -1, 6)$ then $l + m + n=$<br/>

Question 26 :
Which of the triplet can not represent direction cosine of a line

Question 27 :
<span>If $\cos { \alpha ,\quad \cos { \beta ,\quad \cos { \gamma&#160; }&#160; }&#160; }$&#160; &#160;are the direction cosine of a line, then find the value of ${ cos }^{ 2 }\alpha +\left( \cos { \beta +\sin { \gamma&#160; }&#160; }&#160; \right)$ <br> $\left( \cos { \beta - \sin { \gamma&#160; } }&#160; \right)$</span>

Question 28 :
$\dfrac { x - 2 } { 1 } = \dfrac { y - 3 } { 1 } = \dfrac { z - 4 } { - 1 }$ &amp; $\dfrac { x - 1 } { k } = \dfrac { y - 4 } { 2 } = \dfrac { z - 5 } { 2 }$ are coplanar then k=?<br/>

Question 29 :
If $(1, -2, -2)$ and $(0, 2, 1)$ are direction ratios of two lines, then the direction cosines of a perpendicular to both the lines are