A line has direction ratios $2, k, 6$ with $k > 0$, and the cosine of the angle it makes with the $x$-axis is $\frac{2}{7}$. What is $k$?

Explanation

1. 01

   $l = \frac{2}{\sqrt{4 + k^{2} + 36}} = \frac{2}{7}$, so $\sqrt{40 + k^{2}} = 7$.

2. 02

   $k^{2} = 49 - 40 = 9$, and $k > 0$ gives $k = 3$.