Introduction to...

If the orthocentre, circumcentre of a triangle are $$(-3, 5, 2), (6, 2, 5)$$ respectively then the centroid of the triangle is

If $$\mathrm{A}= (-1,6, 6)$$ , $$\mathrm{B}=(-4,9, 6)$$ , $$\displaystyle \mathrm{G}=\frac{1}{3}(-5,22,22)$$ and $$\mathrm{G}$$ is the centroid of the $$\Delta \mathrm{A}\mathrm{B}\mathrm{C}$$ then the name of the triangle $$\mathrm{A}\mathrm{B}\mathrm{C}$$ is

The extremities of a diagonal of a rectangular parallelopiped whose faces are parallel to the reference planes are $$(-2, 4, 6)$$ and $$(3, 16, 6)$$. The length of the base diagonal is

In the tetrahedron $$ABCD,\ A= (1, 2, -3)$$ and $$G(-3,4, 5)$$ is the centroid of the tetrahedron. If $$P$$ is the centroid of the $$\Delta BCD$$, then $$AP=$$

In the $$\Delta $$ ABC , A $$=$$ (1, 3, -2) and G (-1, 4, 2) is the centroid of the triangle. If D is the mid point of BC then AD $$=$$

The harmonic conjugate of $$(2, 3, 4)$$ with respect to the points $$(3, -2, 2)$$ and $$(6, -17, -4)$$ is

$$A = (2, 3, 0)$$ and $$B = (2,1, 2)$$ are two points. If the points $$P, Q$$ are on the line $$AB$$ such that $$AP= PQ = QB$$, then $$PQ=$$

If the points $$A,B,C,D$$ are collinear and $$C,D$$ divide $$AB$$ in the ratios $$2:3, -2:3$$ respectively, then the ratio in which $$A$$ divides $$CD$$ is

Then the correct matching is

$$P (1,1,1 )$$ and $$Q(\lambda, \lambda, \lambda)$$ are two points in the space such that $$PQ=\sqrt{27}$$, then the value(s) of $$\lambda $$ can be