Introduction to...

A point on the line $$\displaystyle \frac{{x + 2}}{1} = \frac{{y - 3}}{{ - 4}} = \frac{{z - 1}}{{2\sqrt 2 }}$$ at a distance 6 from the point (2, 3, 1) is

If $$A (1, 2, 3),  B ( 2, 3, 1),  C (3, 1, 2)$$ then the length  of the altitude through $$C$$ is 

A plane intersects the co ordinate axes at $$A, B, C$$. If $$O= (0, 0, 0)$$ and $$(1, 1, 1)$$ is the centroid of the tetrahedron $$O ABC$$, then the sum of the reciprocals of the intercepts of the plane

The plane $$ax+by+cz+(-3)=0$$ meet the co-ordinate axes in A,B,C. Then centroid
of the triangle is

The name of the figure formed by the points $$(-1, -3, 4), (5, -1,1), (7, -4, 7)$$ and $$(1, -6, 10)$$ is a

The end points of a body diagonal of a rectangular parallelepiped whose faces are parallel to the coordinate planes are $$(2, 3, 5)\ and\ (5, 7, 10)$$. The lengths of its sides are 

A tetrahedron is a three dimensional figure bounded by non coplanar triangular planes. So, a tetrahedron has four non-coplanar points as its vertices. Suppose a tetrehedron has points A,B,C,D as its vertices which have coordinates $$(x1, y1, z_{1}) (x_{2}, y_{2}, z_{2})$$ , $$(x_{3}, y_{3}, z_{3})$$ and $$(x_{4}, y_{4}, z_{4})$$, respectively in a rectangular three dimensional space. Then, the coordinates of its centroid are $$[\dfrac{x_{1}+x_{2}+x_{3}+x_{4}}{4},\dfrac{y_{1}+y_{2}+y_{3}+y_{4}}{4},\dfrac{z_{1}+z_{2}+z_{3}+z_{4}}{4}]$$.
Let a tetrahedron have three of its vertices represented by the points $$(0,0,0) ,(6,5,1)$$ and $$(4,1,3)$$ and its centroid lies at the point $$(1,2,5)$$. Now, answer the following question. The coordinate of the fourth vertex of the tetrahedron is:

If the extremities of a diagonal of a square are $$(1, -2, 3)$$ and $$(4, 2, 3)$$ then the area of the square is

The equation of median through C to side AB is

From which of the following the distance of the point $$(1, 2, 3)$$ is $$\sqrt{10}$$?