Introduction to...

lf $$OABC$$ is a tetrahedron such that the $$OA^{2}+BC^{2}=OB^{2}+CA^{2}=OC^{2}+AB^{2}$$, then which of the following is/are correct

The plane $$\displaystyle ax + by + cz + (-3) = 0$$ meet the co-ordinate axes in $$A, B, C$$. The centroid of the triangle is

If the vertices of a triangle are $$(-1,6,-4),(2,1,1)$$ and $$(5,-1,0)$$ then the centroid of the triangle is

The coordinates of a point which is equidistant from the point $$(0,0,0),(a,0,0),(0,b,0)$$ and $$(0,0,c)$$ are given by

If $$A= \left ( 0,0,2 \right ),B= \left (\sqrt{2},\sqrt{2},2 \right ),C= \left ( \sqrt{2},\sqrt{2},0 \right )$$ and $$D= \left ( \displaystyle \frac{8\sqrt{2}-20}{17},\frac{12\sqrt{2}+4}{17},\frac{20-8\sqrt{2}}{17} \right )$$, then $$ABCD$$ is a

The equation of motion of a rocket are: $$x=2t,y=-4t,z=4t,$$ where the time $$t$$ is given in seconds and the coordinate of a moving point in kilometers. At what distance will the rocket be from the starting point $$O(0,0,0)$$ in $$10$$ seconds ?

What is the distance in space between $$(1,0,5)$$ and $$(-3,6,3)$$?

A triangle $$ABC$$ is placed so that the midpoints of its sides are on the $$x, y$$ and $$z$$ axes respectively. Lengths of the intercepts made by the plane containing the triangle on these axes are respectively $$\displaystyle \alpha ,\beta ,\gamma$$, then the coordinates of the centroid of the triangle $$ABC$$ are

Point A is $$\displaystyle a+2b,$$ and a divides AB in the ratio 2 : 3. The position vector of B is