Introduction to...

The points $$(4, -5, 1)$$, $$(3, -4, 0)$$, $$(6, -7, 3)$$, $$(7, -8, 4)$$ are vertices of a

Four vertices of a tetrahedron are $$(0,0,0),(4,0,0),(0,-8,0)$$ and $$(0,0,12)$$,Its centroid has the coordinates

In geometry, we take a point, a line and a plane as undefined terms.

A rectangular parallelopiped is formed by drawing planes through the points $$(-1,2,5)$$ and $$(1,-1,-1)$$ and parallel to the coordinate planes. the length of the diagonal of the parallelopiped is

The ratio of $$yz$$-plane divide the line joining the points $$A(3, 1,- 5), B(1, 4, -6)$$ is

Let the distance between vectors are given as follows :
$$(i)4i +3j-6k, -2i+j-k$$  be $$\displaystyle \sqrt{k}$$
$$(ii) -2i+3j+5k, 7i-k $$  be  $$\displaystyle m\sqrt{n}$$
Find $$k-(m*n)$$ ?

$$A, B, C$$ are three points on the axes of $$x, y$$ and $$z$$ respectively at distance $$a, b, c$$ from the origin $$O$$; then the co - ordinates of the point which is equidistant from $$A, B, C$$ and $$O$$ is

If the centroid of the tetrahedron $$OABC$$, where $$A, B ,C$$ are given by $$\displaystyle (\alpha, 5, 6), (1, \beta, 4), (3, 2, \gamma)$$ respectively be $$1, -1, 2$$, then value of $$\displaystyle \alpha^2 + \beta^2 + \gamma^2$$ equals

Find the ratio in which the yz-plane divides the join of the points $$\displaystyle \left ( -2,4,7 \right )$$ and $$\displaystyle \left ( 3,-5,8 \right )$$ and also find the co-ordinates of the point of intersection of this line with the $$yz$$ - plane.

Perimeter of triangle whose vertices are $$(0,4,0), (3,4,0)$$ and $$(0,4,4)$$, is