Introduction to...

Ratio in which the $$xy-$$plane divides the join of $$(1, 2, 3)$$ and $$(4, 2, 1)$$ is 

The equation of the set of points which are equidistant from the points $$(1, 2, 3)$$ and $$(3, 2, -1)$$.

$$A(3, 2, 0), B(5, 3, 2), C(-9, 6, -3)$$ are three points forming a triangle. If $$AD$$, the bisector of $$\angle BAC$$ meets $$BC$$ in $$D$$ then coordinates of $$D$$ are

$$A=\left(2,4,5\right)$$ and $$B=\left(3,5,-4\right)$$ are two points. If the $$xy$$-plane,  $$yz$$-plane divide $$AB$$ in the ratios $$a:b,p:q$$ respectively then $$\dfrac{a}{b}+\dfrac{p}{q}$$=

If $$z = \cos \dfrac{\pi }{6} + i\sin \dfrac{\pi }{6}$$, then

The x-coordinate of a point on the line joining the points $$P(2,2,1)$$ and $$Q(5,1,-2)$$ is $$4$$. Find its z-coordinate.

The distance between (5,1,3) and the line x=3, y=7+t, z=1+t is

The perimeter of triangle with vertices at $$(1,0,0) , (0,1,0) and (0,0,1)$$ is :

If the points $$A(9, 8, -10), B(3, 2, -4)$$ and $$C(5, 4, -6)$$ be collinear, then the point $$C$$ divides the line $$AB$$ in the ratio