Find the distance between the following pairs of points:
(i) \((2, 3, 5)\) and \((4, 3, 1)\)
(ii) \((-3, 7, 2)\) and \((2, 4, -1)\)
(iii) \((-1, 3, -4)\) and \((1, -3, 4)\)
(iv) \((2, -1, 3)\) and \((-2, 1, 3)\)
(i) \(2\sqrt{5}\)
(ii) \(\sqrt{43}\)
(iii) \(2\sqrt{26}\)
(iv) \(2\sqrt{5}\)
Show that the points \((-2, 3, 5)\), \((1, 2, 3)\) and \((7, 0, -1)\) are collinear.
Verify the following:
(i) \((0, 7, -10), (1, 6, -6)\) and \((4, 9, -6)\) are the vertices of an isosceles triangle.
(ii) \((0, 7, 10), (-1, 6, 6)\) and \((-4, 9, 6)\) are the vertices of a right angled triangle.
(iii) \((-1, 2, 1), (1, -2, 5), (4, -7, 8)\) and \((2, -3, 4)\) are the vertices of a parallelogram.
Find the equation of the set of points which are equidistant from the points \((1, 2, 3)\) and \((3, 2, -1)\).
\(x - 2z = 0\)
Find the equation of the set of points \(P\), the sum of whose distances from \(A(4, 0, 0)\) and \(B(-4, 0, 0)\) is equal to 10.
\(9x^2 + 25y^2 + 25z^2 - 225 = 0\)