Introduction to...

If $$A(2, 2, -3), B(5, 6, 9), C(2, 7, 9)$$ be the vertices of a triangle. The internal bisector of the angle $$A$$ meets $$BC$$ at the point $$D$$, then find the coordinates of $$D$$.

If the lines $$\frac{x - 0}{1} =\frac{y+1}{2}=\frac{z-1}{-1}$$ and $$\frac{x+1}{k}=\frac{y-3}{-2}=\frac{z-2}{1}$$ are at right angles, then the value of k is

The graph of the equation $$y^{2}+z^{2}=0$$ in three dimensional space is

The area of triangle whose vertices are $$(1, 2, 3), (2, 5, -1)$$ and $$(-1, 1, 2)$$ is

A tangent to the curve $$y = f(x)$$ at $$p(x, y)$$ meets $$x - axis$$ at $$A$$ and $$y-axis$$ at $$B$$. If $$\overline {AP} : \overline {BP} = 1 : 3$$ and $$f(1) = 1$$ then the curve also passes through the point.

If the distance between a point $$P$$ and the point $$(1, 1, 1)$$ on the line $$\dfrac {x - 1}{3} = \dfrac {y - 1}{4} = \dfrac {z - 1}{12}$$ is $$13$$, then the coordinates of $$P$$ are

The values of a for which $$(8, -7, a), (5, 2, 4)$$ and $$(6, -1, 2)$$ are collinear, is given by?

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

The ratio in which the line joining points $$(2,4,5)$$ and $$(3,5,-4)$$ divide YZ -plane is 

The points $$(10,7,0)$$, $$(6,6-1)$$ and $$(6,9,-4)$$ form a