If the distance between the points A(- 1, 3, - 4) and B(1, - 3, a) is \(2\sqrt{26}\) then find the possible values of a?

Question

Question

Answer 1

CONCEPT:

CALCULATION:

Given: The distance between the points A(- 1, 3, - 4) and B(1, - 3, a) is \(2\sqrt{26}\)

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 = -1, y1 = 3, z1 = -4, x2 = 1, y2 = - 3, z2 = a and \(d = 2\sqrt{26}\)

⇒ \(2\sqrt {26} = \sqrt {(1+1)^2 + (-3 - 3)^2 + (a + 4)^2}\)

⇒ \(2\sqrt {26} = \sqrt {4 + 36 + (a + 4)^2}\)

By squaring both the sides we get,

⇒ 104 = 40 + a² + 8a + 16

⇒ a² + 8a - 48 = 0

⇒ a = 4, - 12

Hence, correct option is 2.