1. ## Direction of Angles

Not sure what to do here:

The direction angles of a vector are all equal. Find the direction angles to the nearest degree.

2. Hello, Neconine!

The direction angles of a vector are all equal.
Find the direction angles to the nearest degree.

The direction angles of a vector are $\alpha,\:\beta,\:\gamma$, which are the angles
. . formed by the vector and the $x.\:y,$ and $z$ axes, respectively.

Fact: . $\cos^2\!\alpha + \cos^2\!\beta + \cos^2\!\gamma \:=\:1$

Since $\alpha = \beta = \gamma$ we have: . $\cos^2\!\alpha + \cos^2\!\alpha + \cos^2\!\alpha \;=\;1$

. . $3\cos^2\!\alpha \:=\:1 \quad\Rightarrow\quad \cos^2\!\alpha \:=\:\frac{1}{3} \quad\Rightarrow\quad \cos\alpha \:=\:\frac{1}{\sqrt{3}}$
. . $\alpha \;=\;\cos^{-1}\left(\frac{1}{\sqrt{3}}\right) \;=\;54.73561032^o$

Therefore: . $\alpha \;=\;\beta\;=\;\gamma \;\approx\;55^o$