Introduction to...

Calculate the distance between the points $$(-3,6,7)$$ and $$(2,-1,4)$$ in $$3D$$ space.

An equation of sphere with centre at origin and radius $$r$$ can be represented as

The ratio in which the line joining $$(2, -4, 3)$$ and $$(-4, 5, -6)$$ is divided by the plane $$3x+2y+z-4=0$$ is

If the distance between the points $$(7,1,-3)$$ and $$(4,5,\lambda)$$ is $$13$$ units, then what is one of the values of $$\lambda$$?

The planes $$2x - y + 4z = 5$$ and $$5x - 2.5y + 10z = 6$$ are

The equation of plane passing through $$(-1,0,-1)$$ parallel to $$xz$$ plane is

The distance of the point $$P(a, b, c)$$ from the $$x$$-axis is.

If a line $$OP$$ of length $$r$$ (Where '$$O$$' is the origin) makes an angle $$\alpha$$ with x-axis and lies on the xz-plane, then what are the coordinates of $$P$$?

Points $$A(3,2,4),B\left( \cfrac { 33 }{ 5 } ,\cfrac { 28 }{ 5 } ,\cfrac { 38 }{ 5 }  \right) $$, and $$C(9,8,10)$$ are given. The ratio in which $$B$$ divides $$\overline { AC } $$ is

The locus of a point, which is equidistant from the points $$(1, 1)$$ and $$(3, 3)$$, is