Introduction to...

If two vertices of an equilateral triangle are $$(2, 1, 5)$$ and $$(3, 2, 3)$$, then its third vertex is:

The point which is equidistant from the points $$(-1, 1, 3), (2, 1, 2), (0, 5, 6)$$ and $$(3,2, 2)$$ is

The point which is equidistant from the points $$(a, 0, 0), (0, b, 0), (0, 0, c)$$ and $$(0, 0, 0)$$ is:

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

If $$A, B$$ are the feet of the perpendiculars from $$(2, 4, 5)$$ to the $$x$$-axis, $$y$$-axis respectively, then the distance $$AB$$ is

If $$A(0, 4, 1), B(a, b, c), C(4, 5, 0), D(2, 6, 2)$$ are the consecutive vertices of a square, then the distance $$BD$$ is:

If $$(p, q, r)$$ is equidistant from $$(1, 2, -3), (2, -3, 1)$$ and $$(-3, 1, 2)$$, then $$p +q + r$$ $$=$$

$$A = (1, -1, 2)$$ and $$B =$$ $$(2, 3, 7)$$ are two points. lf $$P,\ O$$ divide $$AB$$ in the ratios $$2:3, -2:3$$ respectively then $$P_x+Q_y=$$

$$\mathrm{If}   \mathrm{A}=(1, 2, 3)$$ , $$\mathrm{B}=(2,3, 4)$$ and $$\mathrm{C}$$ is a point of trisection of$$\mathrm{A}\mathrm{B}$$ such that $$\displaystyle \mathrm{C}_{\mathrm{x}}+\mathrm{C}_{\mathrm{y}}=\frac{13}{3}$$ then $$\mathrm{C}_{\mathrm{z}}=$$

$$A=(2, 4, 5)$$ and $$B=(3,5, -4)$$ are two points. lf the $$XY$$-plane, $$YZ$$-plane divide $$AB$$ in the ratio $$a:b$$ and $$ p:q$$ respectively, then $$\dfrac {a}{b}+\dfrac {p}{q}=$$