Question

The distance of the point P (a, b, c) from the x-axis is
(a) $\sqrt{b^2+c^2}$

(b) $\sqrt{a^2+c^2}$

(c) $\sqrt{a^2+b^2}$

(d) none of these

Answer 1

$$\begin{gathered} \left(\mathrm{a}\right)\sqrt{b^2+c^2} \\ \mathrm{The}\mathrm{projection}\mathrm{of}\mathrm{the}\mathrm{point}P\left(a,b,c\right)\mathrm{on}\mathrm{the}x-\mathrm{axis}\mathrm{is}\left(a,0,0\right)\mathrm{as}\mathrm{both}Y\mathrm{and}Z\mathrm{coordinates}\mathrm{on}\mathrm{any}\mathrm{point}\mathrm{on}\mathrm{the}x-\mathrm{axis}\mathrm{are}\mathrm{equal}\mathrm{to}\mathrm{zero}. \\ \therefore \mathrm{Distance}\mathrm{of}P\mathit{}\left(a\mathit{,}\mathit{}b\mathit{,}\mathit{}c\right)\mathit{}\mathrm{from}x-\mathrm{axis}=\mathrm{Distance}\mathrm{of}P\mathit{}\left(a\mathit{,}\mathit{}b\mathit{,}\mathit{}c\right)\mathit{}\mathrm{from}\left(\mathrm{a},0,0\right) \\ =\sqrt{{\left(a\mathit{-}a\right)}^2+{\left(b\mathit{-}0\right)}^2+{\left(c-0\right)}^2} \\ =\sqrt{b^2+c^2} \end{gathered}$$