Introduction to...

Plane $$ax + by + cz = 1$$ intersect axes in $$A, B, C$$ respectively. If $$G\left (\dfrac {1}{6}, -\dfrac {1}{3}, 1\right )$$ is a centroid of $$\triangle ABC$$ then $$a + b + 3c =$$ _________.

If $$xy-$$plane and $$yz-$$plane divides the line segment joining $$A(2,4,5)$$ and $$B(3,5,-4)$$ in the ratio $$a:b$$ and $$p:q$$ respectively then value of $$\left(\dfrac {a}{b}+\dfrac {p}{q}\right)$$ may be

Locus of a point $$P$$ which such that $$PA = PB$$ where $$A = (0, 3, 2)$$ and $$B = (2, 4, 1)$$ is

Points $$(5, 0, 2), (2, -6, 0), (4, -9, 6)$$ & $$(7, -3, 8)$$ are vertices of a 

The values of a for which $$(8,-7,a),(5,2,4)$$ and $$(6,-1,2)$$ are collinear , is given by 

Given $$A(3, 2, -4), B(5, 4, -6)$$ & $$C(9, 8, -10)$$ are collinear. Ratio in which $$B$$ divides $$AC$$

A cube of side 5 has one vertex at the point (1,0,-1), and the three edges from this vertex are, respectively, parallel to the negative x and y axes and positive  z-axis. Find the coordinates of the other vertices of the cube.

If $$O=(0,0,0),OP=5$$ and the d.rs of OP are $$1,2,2$$ then $$P_x+P_y+P_z=$$

Find the co-ordinates of a point lying on the line $$\dfrac{x -2}{3} = \dfrac{y + 3}{4} = \dfrac{z - 1}{7}$$ which is at a distance $$10$$ units from $$(2, -3, 1)$$.

The ratio in which the join of $$(1, -2, 4)$$ and $$(4, 2, -1)$$ divided by the $$XY$$ plane is