Question 1 :
Assertion ($A$): The points with position vectors $\overline{a},\overline{b},\overline{c}$ are collinear if $2\overline{a}-7\overline{b}+5\overline{c}=0$.<br/>Reason ($R$): The points with position vectors $\overline{a},\overline{b},\overline{c}$ are collinear if $l\overline{a}+m\overline{b}+n\overline{c}=\overline{0}$.<br/>
Question 2 :
If $\vec { a } ,\vec { b } ,\vec { c } $ are three non-zero vectors, no two of which are collinear and the vector $\vec { a } +\vec { b }$ is collinear with $\vec { c }, \vec { b } +\vec { c } $ is collinear with $\vec {a},$ then $\vec { a } +\vec { b } +\vec { c }$ is equal to -
Question 3 :
A line makes angles $\alpha$, $\beta $, $\gamma $ with the positive directions of the axes of reference. The value of $\cos 2\alpha +\cos 2\beta +\cos<br/>2\gamma$ is<br/>
Question 4 :
If ${ l }_{ 1 },{ m }_{ 1 },{ n }_{ 1 }$ and ${ l }_{ 2 },{ m }_{ 2 },{ n }_{ 2 }$ are DCs of the two lines inclined to each other at an angle $\theta$, then the DCs of the internal bisector of the angle between these lines are
Question 5 :
The line passing through the points $10\hat{i}+3\hat{j}$, $ 12\hat{i}+5\hat{j}$ also passes through the point $a\hat{i}+11 \hat{j}$, then $a=$<br/>
Question 6 :
If $\overline{a}$ and $\overline{b}$ are two non-collinear vectors, then the points $l_{1}\overline{a}+m_{1}\overline{b}$, $  l_{2}\overline{a}+m_{2}\overline{b}$ and $l_{3}\overline{a}+m_{3}\overline{b}$ are collinear if<br/>
Question 7 :
The direction cosines to two lines at right angles are (1,2,3) and (-2,$\frac{1}{2}$,$\frac{1}{3}$), then the direction cosine perpendicular to both given lines are:
Question 8 :
$A=(-1, 2, -3), B=(5, 0, -6), C=(0, 4, -1)$ are the vertices of a triangle. The d.c's of the internal bisector of $\angle$BAC are?
Question 9 :
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)
Question 10 :
The direction ratios of thenormal to the plane through $(1,0,0)$ and $(0,1,0)$ which makes an angle of $\dfrac{\pi }{4}$ with the plane $x + y = 3$ are-
Question 11 :
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 12 :
Direction ratio of two lines are $l_{1}, m_{1},n_{1}$ and $l_{2},m_{2},n_{2}$ then direction ratios of the line perpendicular to both the lines are
Question 13 :
If the position vectors of the points $A$, $B$, and $C$ be $i + j $ , $i - j$ and $ai + bj+ ck$ respective;y , then the points $A$, $B$ and $C$ are collinear if:
Question 14 :
The projection of a directed line segment on the co-ordinate axes are $12, 4, 3$, the DC's of the line are<br/>