Let $S$ be the subset in $\mathbb{R}^3$ of all vectors forming an angle $ \leq 45^{\circ}$ with the vector $(1 , 0 , 1)^T.$
I have no idea how to approach this problem?
Is this the right approach, $S=\{X=(x,y,z) \in \mathbb{R}^3 \mid X.(1,0,1) \leq ||X||.||(1,0,1)||.\cos45^{\circ}\}$