Introduction to...

The value(s) of $$\lambda $$, for which the triangle with vertices $$(6,10,10),(1,0,-5)$$ and $$(6,-10,\lambda)$$ will be a right angled triangle is/ are

$$P(0,5,6),Q(1,4,7),R(2,3,7)$$ and $$S(3,5,16)$$ are four points in the space. The point nearest to the origin $$O(0,0,0)$$ is

If $$A(\cos\alpha,\sin\alpha, 0),B(\cos\beta,\sin\beta, 0)$$, $$C(\cos\gamma,\sin\gamma,0)$$ are vertices of $$\Delta ABC$$ and let 

Arrange the points: $$\mathrm{A}(1,2-3), \mathrm{B}(-1,2,-3), \mathrm{C}(-1,-2-3)$$ and $$\mathrm{D}(1,-2, -3)$$ in the increasing order of their octant numbers:

In the $$\Delta ABC$$, if $$AB=\sqrt{2}; AC=\sqrt{20}, B=(3,2,0)$$ and $$C=(0,1,4)$$, then the length of the median passing through $$A$$ 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

Assertion (A): The points $$A(2,9,12) ,B(1,8,8) ,C(2,11,8) D(1,12,12)$$ are the vertices of a rhombus
Reason (R): $$AB = BC = CD = DA$$ and $$AC = BD$$

If the plane a  $$2x-3y+5_{Z}-2=0$$ divides the line segment joining $$(1, 2, 3)$$ and $$(2, 1, k)$$ in the ratio $$9 : 11$$, then $$k$$ is

The point equidistant from the points $$(0,0,0), (1,0,0), (0,2,0)$$ and $$(0,0,3)$$ is

Assertion(A): If centroid and circumcentre of a triangle are known its orthocentre can be found.
Reason (R) : Centriod, orthocentre and circumcentre of a triangle are collinear