Introduction to...

A $$= (1, 1, 4)$$ and B $$= (5,-3, 4)$$ are two points. If the points $$P$$, $$Q$$ are on the line AB such that AP $$=$$ PQ $$=$$ QB then PQ $$=$$

If P $$(3, 2, -4)$$ , Q $$(5, 4, -6)$$ and R $$(9, 8, -10)$$ are collinear, then R divides PQ in the ratio

The distance from the origin to the centroid of the tetrahedron formed by the points $$(0, 0, 0), (3, 0, 0), (0, 4, 0), (0, 0, 5)$$ is 

The position vectors of the four angular point of a tetrahedron $$OABC$$ are $$(0, 0, 0)$$; $$(0, 0, 2)$$; $$(0, 4, 0)$$ and $$(6, 0, 0)$$ respectively. Find the coordinates of cenroid

Let $$A= \left ( 1,2,3 \right )B= \left ( -1,-2,-1 \right )C= \left ( 2,3,2 \right )$$ and $$ D= \left ( 4,7,6 \right )$$. Then $$ABCD$$ is a

If $$A= \left ( 5,-1,1 \right ),B= \left ( 7,-4,7 \right ),C= \left ( 1,-6,10 \right ),D= \left ( -1,-3,4 \right )$$. Then $$ABCD$$ is a

The equation of the plane which is parallel to the $$xy-$$plane is

The distance of the point $$(1,-2,3)$$ from  the plane $$x-y+z=5$$ measured parallel to the line $$\displaystyle \frac{x}{2}=\displaystyle \frac{y}{3}=\displaystyle \frac{z}{-6}$$ is

If  $$C_1:{x^2+y^2}-20x+64=0$$ and $$C_2:{x^2+y^2}+30x+144=0$$. Then the length of the shortest line segment $$PQ$$  which touches $$C_1$$ at $$P$$ and  to  $$C_2$$ at $$Q$$ is

The plane $$XOZ$$ divides the join of $$(1,-1,5)$$ and $$(2,3,4)$$ in the ratio $$\lambda :1$$, then $$\lambda$$ is