Find the distance between the points P (6, 4, - 3) and Q (2, - 8, 3) ?

CONCEPT:

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

CALCULATION:

Given: P (6, 4, - 3) and Q (2, - 8, 3) are two points in a 3D space.

Here, we have to find the distance between the the given points.

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

⇒ \(d = \sqrt {(-4)^2+(-12)^2+(6)^2}\)

\(d = \sqrt {{{\left( {{2} - {6}} \right)}^2} + {{\left( {{-8} - {4}} \right)}^2} + {{\left( {{3} + {3}} \right)}^2}} = 14 \ units\)