Question

If the position vector \[\vec{a}\] of a point (12, n) is such that \[\left| \vec{a} \right|\] = 13, find the value (s) of n.

Answer 1

Given a position vector \[\vec{a}\]  of a point \[\left( 12, n \right)\]  such that, \[\vec{a} = 12 i^\land + n j^\land\] Then, \[\left| \vec{a} \right| = \sqrt{{12}^2 + n^2}\]
Also,
\[\left| \vec{a} \right| = 13\]   (given)
Thus, we get,
\[\sqrt{{12}^2 + n^2} = 13\]
\[ \Rightarrow {12}^2 + n^2 = 169\]
\[ \Rightarrow n^2 = 169 - 144\]
\[ \Rightarrow n^2 = 25\]
\[ \Rightarrow n = \pm 5\]