Question

If the distance between (a, 2, 1) and (1, –1, 1) is 5, then a = _____________________.

Answer 1

Let A be represented by (a, 2, 1) and B be represented by (1, –1, 1)
Since distance between AB = 5
$$\begin{gathered} \mathrm{i}.\mathrm{e}\sqrt{{\left(a-1\right)}^2+{\left(2+1\right)}^2+{\left(1-1\right)}^2}=5 \\ \mathrm{i}.\mathrm{e}\sqrt{{\left(a-1\right)}^2+9}=5 \end{gathered}$$
By squaring both sides,
i.e (a – 1)² + 9 = 25
i.e a² + 1 – 2a + 9 – 25 = 0
i.e a² – 2a – 15 = 0
i.e a² + 3a – 5a – 15 = 0
i.e a(a + 3) –5 (a + 3) = 0
i.e a = 5 or a = –3