Question 1 :
The coordinate of any point, which lies in $xy$ plane , is
Question 2 :
State the following statement is True or False<br/>If two distinct lines are intersecting each other in a plane then they cannot have more than one point in common.<br/>
Question 4 :
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 7 :
$A(3, 2, 0), B(5, 3, 2), C(-9, 6, -3)$ are three points forming a triangle. If $AD$, the bisector of $\angle BAC$ meets $BC$ in $D$ then coordinates of $D$ are
Question 8 :
The ratio in which the plane $2x+3y-2z+7=0$ divides the line segment joining the points $(-1, 1, 3)$, $(2, 3, 5)$ is
Question 9 :
$A=\left(2,4,5\right)$ and $B=\left(3,5,-4\right)$ are two points. If the $xy$-plane, $yz$-plane divide $AB$ in the ratios $a:b,p:q$ respectively then $\dfrac{a}{b}+\dfrac{p}{q}$=
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 :
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 13 :
If the $zx$-plane divides the line segment joining $(1,-1,5)$ and $(2,3,4)$ in the ratio $p:1$, then $p+1=$
Question 14 :
In three dimensions, the coordinate axes of a rectangular cartesian coordinate system are
Question 16 :
If the line joining $A(1, 3, 4)$ and $B$ is divided by the point $(-2, 3, 5)$ in the ratio $1 : 3$, then $B$ is<br/>
Question 17 :
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 18 :
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 19 :
Find the ratio in which (the plane) $2x+3y+5z=1$ divides the line joining the points $(1,0,-3)$ and $(1,-5,7)$.
Question 20 :
If the centroid of tetrahedron $OABC$ where $A,B,C$ are given by $(a,2,3), (1,b,2)$ and $(2,1,c)$ respectively is $(1,2,-2)$, then distance of $P(a,b,c)$ from origin is<br/>
Question 21 :
A plane intersects the co ordinate axes at $A, B, C$. If $O= (0, 0, 0)$ and $(1, 1, 1)$ is the centroid of the tetrahedron $O ABC$, then the sum of the reciprocals of the intercepts of the plane<br/>
Question 22 :
If $P(x,y,z)$ is a point on the line segment joining $Q(2,2,4)$ and $R(3,5,6)$ such that the projection of $\overrightarrow { OP } $ on the axes are $\displaystyle \frac { 13 }{ 5 } ,\frac { 19 }{ 5 } ,\frac { 26 }{ 5 } $ respectively, then $P$ divides $QR$ in ratio
Question 23 :
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 24 :
If the $zx$-plane divides the line segment joining $(1, -1, 5)$ and $(2, 3, 4)$ in the ratio $p : 1$, then $p + 1=$<br/>
Question 25 :
If $P\left( x,y,z \right) $ is a point on the line segment joining $Q\left( 2,2,4 \right) $ and $R\left( 3,5,6 \right) $ such that the projection of $\overline { OP } $ on the axes are $\displaystyle\frac { 13 }{ 5 } ,\frac { 19 }{ 5 } ,\frac { 26 }{ 5 } ,$ respectively, then $P$ divides $QR$ in the ratio