Find the distance between the points A(2, - 1, 3) and B(-2, 1, 3) ?

CONCEPT:

• The distance between the points A(x1, y1, z1) and B(x2, y2, z2) is given by: \(d = \sqrt {(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}\)

CALCULATION:

Given: A(2, - 1, 3) and B(-2, 1, 3) are two points in a 3D plane.

Let d denote the distance between the given points.

As we know that, the distance between the points A(x1, y1, z1) and B(x2, y2, z2) is given by: \(d = \sqrt {(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}\)

Here, x1 = 2, y1 = - 1, z1 = 3, x2 = - 2, y2 = 1 and z2 = 3.

⇒ \(d = \sqrt {(-2 - 2)^2 + (1 + 1)^2 + (3 - 3)^2}\)

⇒ \(d = 2\sqrt 5\)

Hence, correct option is 1.