Question

The distance between the points (1, 3, 4) and (-4, 1, 2) is

(A) \(\sqrt 5\)

(B) \(2\sqrt 5\)

(C) \(3\sqrt 5\)

(D) \(4\sqrt 5\)

Answer 1

Correct option is (C) \(3\sqrt 5\)

Distance between two points \((x_1, y_1, z_1)\) and \((x_2, y_2, z_2)\) can be given as

\(D =\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}\)

∴ Distance between \((1, - 3, 4)\) and \((-4, 1, 2)\) is

\(D = \sqrt{(- 4 - 1)^2 + (1 - (-3))^2 + (2 - 4)^2}\)

\(= \sqrt{(-5)^2 + (4)^2 + (-2)^2}\)

\(= \sqrt{25 + 16 + 4}\)

\(= \sqrt{45}\)

\(= 3 \sqrt 5\)