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