Introduction to...

If A = (2,-3,1), B = (3,-4,6) and C is a point of trisection of AB, then $${ C }_{ y }$$

The coordinates of the orthocentre of the triangle that has the coordinates of mid points of its sides as (0 , 0) (1 , 2) and ( -6 , 3) is : 

Consider a variable plane $$lx+my+nz=k(k>0)and\quad l,m,n$$ are direction cosines of normal of the plane. Let the given plane intersects the co-ordinate axes at A,B and C, then the minimum area of $$\triangle ABC$$ is _______.

The shortest distance between the point $$\left( \dfrac { 3 }{ 2 } ,0 \right) $$ and the curve $$y=\sqrt { x } $$, $$(x>0)$$, is:

If $$A=(1, 2, 3)$$ and $$B(3, 5, 7)$$ and P, Q are the points on AB such that AP$$=$$PQ$$\neq$$QB, then the mid point of PQ is?

If $$A=(1, -2, -1), B=(4, 0, -3); C=(1, 2, -1)$$ and $$D=(2, -4, -5)$$, then the distance between AB and CD is?

The equation of plane which is passing through the point $$(1,2,3)$$ and which is at maximum distance from the point $$(-1,0,2)$$ is

The distance of the point $$(2,1,-1)$$ from the line $$\dfrac{x-1}{2}=\dfrac{y+1}{1}=\dfrac{z-3}{-3}$$ measured parallel to the plane $$x+2y+z=4$$ is

A line passes through two points A(2, -3, -1) and B(8, -1, 2) the coordinates of a point on this line nearer to the origin at a distance of 14 units from A are