Question

If the distance between the points P(a, 2, 1) and Q (1, −1, 1) is 5 units, find the value of a.

Answer 1

PQ = 5
$$\begin{gathered} \Rightarrow \sqrt{{\left(1-a\right)}^2+{\left(-1-2\right)}^2+{\left(1-1\right)}^2}=5 \\ \Rightarrow {\left(1-a\right)}^2+{\left(-3\right)}^2=25 \\ \Rightarrow 1-2a+a^2+9-25=0 \\ \Rightarrow a^2-2a-15=0 \\ \Rightarrow \left(a-5\right)\left(a+3\right)=0 \\ \Rightarrow a=5,-3 \end{gathered}$$