Question

Find the distance between the following pairs of points:
(i) P(1, –1, 0) and Q(2, 1, 2)
(ii) A(3, 2, –1) and B(–1, –1, –1).

Answer 1

(i) PQ = $\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2+{\left(z_2-z_1\right)}^2}$
= $\sqrt{{\left(2-1\right)}^2+{\left(1+1\right)}^2+{\left(2-0\right)}^2}$
= $\sqrt{1^2+2^2+2^2}$
= $\sqrt{1+4+4}$
= $\sqrt{9}$
= 3

(ii) AB = $\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2+{\left(z_2-z_1\right)}^2}$
$$\begin{gathered} =\sqrt{{\left(-1-3\right)}^2+{\left(-1-2\right)}^2+{\left(-1+1\right)}^2} \\ =\sqrt{{\left(-4\right)}^2+{\left(-3\right)}^2+{\left(0\right)}^2} \\ =\sqrt{16+9+0} \\ =\sqrt{25} \\ =5 \end{gathered}$$