Introduction to...

Let $O$ be the origin and $A$ be the point $(64, 0)$. If $P$ and $Q$ divide $OA$ in the ratio $1 : 2 : 3$, then the point $P$ is

The shortest distance between z-axis and the line 
$x+y+2z-3=0=2x+3y+4z-4$, is _____________

If $z_{1}$ and $z_{2}$ are $z$ co-ordinates of the points of trisection of the segment joining the points $A(2, 1, 4), B(-1, 3, 6)$ then $z_{1} + z_{2} =$

The point which divides the line joining the points $(1, 3, 4)$ and $(4,3,1)$ internally in the ratio $2:1 ,$ is 

The distance between the X-axis and the point $(3, 12, 5)$ is

The coordinates of the foot of the perpendicular drawn from the point $A(1,0,3)$ to the join of the points $B(4,7,1)$ and $C(3,5,3)$ are

In the triangle with vertices $A(1, -1, 2), B(5, -6, 2)$ and $C(1,3,-1)$ find the altitude $n=|BD|$.

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

A swimmer can swim $2$ km in $15$ minutes in a lake and in a river he can swim a distance of $4$ km in $20$ minutes along the stream. If a paper boat is put in the river, then the distance covered by it in $\displaystyle$2$\, \frac{1}{2}$2 hours will be 

In a $\triangle {ABC}$, side $AB$ has the equation $2x+3y=29$ and the side $AC$ has the equation $x+2y=16$. If the mid point of $BC$ is $(5,6)$, then the equation of $BC$ is