Introduction to...

Find the ratio in which (the plane) $$2x+3y+5z=1$$ divides the line joining the points $$(1,0,-3)$$ and $$(1,-5,7)$$.

A hall has dimensions $$24 m \times 8 m \times 6 m$$. The length of the longest pole which can be accommodated in the hall is

The coordinates of a point which divides the line joining the points $$P(2,3,1)$$ and $$Q(5,0,4)$$ in the ratio $$1:2$$ are

In $$\triangle ABC$$ the mid points of the sides $$AB, BC$$ and $$CA$$ are respectively $$\left( l,0,0 \right) ,\left( 0,m,0 \right) $$ and $$\left( 0,0,n \right) $$. Then, $$\dfrac { { AB }^{ 2 }+{ BC }^{ 2 }+{ CA }^{ 2 } }{ { l }^{ 2 }+{ m }^{ 2 }+{ n }^{ 2 } } $$ is equal to

The distance of the point (1,−2,4) from the plane passing through the point (1,2,2) and perpendicular to the planes $$x−y+2z=3$$ and $$2x−2y+z+12=0$$ is :

The point $$(3, 0, -4)$$ lies on the

What is the length of the segment in the x-y plane with end points at $$(-2, -2)$$ and $$(2, 3)$$?

Graph $$x^2+y^2=4$$ in 3D looks like

If the line joining $$A(1, 3, 4)$$ and $$B$$ is divided by the point $$(-2, 3, 5)$$ in the ratio $$1 : 3$$, then $$B$$ is

Point $$D$$ has coordinates as $$(3,4,5)$$. Referring to the given figure, find the coordinates of point $$E$$.