Introduction to...

If $$(1, 1, a)$$ is the centroid of the triangle formed by the points $$(1, 2, -3)$$ , $$(\mathrm{b}, 0, 1)$$ and $$(-1, 1, -4)$$ then $$a-b$$ $$=$$

If the extremities of a diagonal of a square are $$(1, -2, 3)$$ and $$(2, -3, 5)$$, then area of the square is

If $$A= (1, 2, 3), B = (2, 3, 4)$$ and $$AB$$ is produced upto $$C$$ such that $$2AB = BC$$, then $$C =$$

If the points $$A(3, -2, 4)$$, $$B(1, 1, 1)$$ and $$C(-1, 4, -2)$$ are collinear, then the ratio in which $$C$$ divides $$AB$$ is 

If $$A = (2, -3, 1), B = (3, -4, 6)$$ and $$C$$ is a point of trisection of $$AB$$, then $${C}_{{y}}=$$

Two opposite vertices of a square are $$(2, -3, 4)$$ and $$(4, 1, -2)$$. The length of the side of the square is

The point $$P$$ is on the $$y$$-axis. If $$P$$ is equidistant from $$(1,2, 3)$$ and $$(2,3, 4)$$, then $$P_{y}=$$

$$A = (1, -2, 3)$$ , $$B =$$ (2, 1, 3), $$C =$$ (4, 2, 1) and $$G= (-1,3, 5)$$ is the centroid of the tetrahedron $$ABCD$$. Then the fourth coordinate is

$$XOZ$$ plane divides the join of $$(2,3,1)$$ and $$(6,7,1)$$ in the ratio

The shortest distance of $$(a,b,c)$$ from $$x$$-axis is