Introduction to...

The ratio in which the line joining $$(3,4,-7)$$ and $$(4,2,1)$$ is dividing the xy-plane

The shortest distance of the point $$(1,2,3)$$ from $${x}^{2}+{y}^{2}=0$$ is 

A triangle $$ABC$$ is placed so that the mid-points of the sides are on the $$x,y,z$$ axes. Lengths of the intercepts made by the plane containing the triangle on these axes are respectively $$\alpha, \beta, \gamma$$. Coordinates of the centroid of the triangle $$ABC$$ are

The distance between two points $$(1,1)$$ and $$\left( {\dfrac{{2{t^2}}}{{1 + {t^2}}},\dfrac{{{{\left( {1 - t} \right)}^2}}}{{1 + {t^2}}}} \right)$$ is 

The points (-5,12), (-2,-3),(9,-10),(6,5) taken in order, form

The plane $$x = 0$$ divides the joinning of $$( - 2, 3, 4)$$ and $$(1, - 2, 3)$$ in the ratio :

The nearest point  from the origin is 

The vertices of a triangle are $$(2, 3, 5), (-1, 3, 2), (3, 5, -2)$$, then the angles are

The plane passing through the point $$\left(-2,-2,2\right)$$ and containing the line joining the points $$\left(1,1,1\right)$$ and $$\left(1,-1,2\right)$$ makes intercepts on the coordinates axes, the sum whose lengths is ?

The points $$(3,\ 2,\ 0),\ (5,\ 3,\ 2)$$ and $$(-9,\ 6,\ -3)$$, are the vertices of a triangle $$ABC.AD$$ is the internal bisector of $$\angle\ BAC$$ which meets $$BC$$ at $$D$$. Then the co-ordinates of $$D$$, are