Question 3 :
In three dimensions, the coordinate axes of a rectangular cartesian coordinate system are
Question 4 :
The coordinate of any point, which lies in $xy$ plane , is
Question 6 :
If $A= (1, 2, 3), B = (2, 3, 4)$ and $AB$ is produced upto $C$ such that $2AB = BC$, then $C =$<br/>
Question 7 :
The points (2, 5) and (5, 1) are the two opposite vertices of a rectangle. If the other two vertices are points on the straight line $y = 2x + k$, then the value of k is
Question 8 :
Plane $ax + by + cz = 1$ intersect axes in $A, B, C$ respectively. If $G\left (\dfrac {1}{6}, -\dfrac {1}{3}, 1\right )$ is a centroid of $\triangle ABC$ then $a + b + 3c =$ _________.
Question 10 :
The ratio in which $xy-$plane divides the line joining the points $(1, 0, -3)$ and $(1, -5, 7)$ is given by
Question 11 :
Three vertices of a tetrahedron are $(0,0,0),(6,-5,-1)$and $(-4,1,3)$. If the centroid of the tetrahedron be$(1,-2,5)$ then the fourth vertex is<br>
Question 12 :
If $P= (0, 0, 0), Q = (3, 6, 9)$ and $R$ is a point of trisection of $PQ$, then $R_y=$<br>
Question 13 :
The ratio in which the line joining $(3,4,-7)$ and $(4,2,1)$ is dividing the xy-plane
Question 14 :
If the points $A(3, -2, 4)$, $B(1, 1, 1)$ and $C(-1, 4, -2)$ are collinear, then the ratio in which $C$ divides $AB$ is <br/>
Question 15 :
$G(1, 1, -2)$ is the centroid of the triangle $ABC$ and $D$ is the mid point of $BC$. If $A = (-1, 1, -4)$, then $D =$<br/>
Question 16 :
In geometry, we take a point, a line and a plane as undefined terms.<br/>
Question 17 :
A $= (1, 1, 4)$ and B $= (5,-3, 4)$ are two points. If the points $P$, $Q$ are on the line AB such that AP $=$ PQ $=$ QB then PQ $=$<br/>
Question 18 :
Four vertices of a tetrahedron are $(0, 0, 0), (4, 0, 0), (0, -8, 0)$ and $(0, 0, 12)$. Its centroid has the coordinates<br/>
Question 19 :
The ratio in which $yz$-plane divides the line segment joining $(-3, 4, 2), (2, 1, 3)$ is<br/>
Question 20 :
If xy -plane and yz-plane divides the line segment joining A(2,4,5) and B(3,5,-4) in the ratio a:b and p:q respectively then value of $\left( {{a \over b},{p \over q}} \right)$  may be<br/>
Question 21 :
Four vertices of a tetrahedron are $(0,0,0),(4,0,0),(0,-8,0)$ and $(0,0,12)$,Its centroid has the coordinates<br>
Question 22 :
Point A is $\displaystyle a+2b,$ and a divides AB in the ratio 2 : 3. The position vector of B is
Question 24 :
The coordinates of the point where the line segment joining $A(5,1,6)$ and $B (3,4,1)$ crosses the yz plane are
Question 25 :
Find the ratio in which $2x + 3y + 5z = 1$ divides the line joining the points $(1,\ 0,\ -3)$ and $(1,\ -5,\ 7)$.
Question 26 :
If the plane $7x + 11y+ 13z= 3003$ meets the axes in $A, B, C$, then the centroid of $\Delta ABC$ is
Question 27 :
The chord of contact of tangents from a point $P$ to a circle passes  through $q$<i>. </i>If $l_1$ and $l_2$ are the lengths of the tangents from $P$ and $Q$ to the circle, then $PQ$ is equal to
Question 28 :
If $P(x,y,x)$ is a point on the line segment joining $Q(2,2,4)$ and $R(3,5,6)$ such that the projection of $\overline { OP } $ on the axis are $\displaystyle \frac { 13 }{ 5 } ,\frac { 19 }{ 5 } ,\frac { 26 }{ 5 } ,$ respectively, then $P$ divides $QR$ in the ratio
Question 30 :
In the triangle with vertices $A(1, -1, 2), B(5, -6, 2)$ and $C(1,3,-1)$ find the altitude $n=|BD|$.<br/>