17) If the direction angles of the straight line are \( \boldsymbol{\theta}_{x}, \boldsymbol{\theta}_{y}, \boldsymbol{\theta}_{z} \), then \( \cos 2 \theta_{x}+\cos 2 \theta_{y}+\cos 2 \theta_{z}= \qquad \) a) -2 b) -1 c) 1 d) 2

Let's delve into the world of direction angles of a straight line! The direction angles \( \theta_{x}, \theta_{y}, \theta_{z} \) correspond to the angles that the line makes with the coordinate axes. One fascinating fact is that the sum of the cosines of the squares of these angles equals one, which forms a crucial part of understanding the geometry of three-dimensional space. Now, to tackle the equation \( \cos 2\theta_{x} + \cos 2\theta_{y} + \cos 2\theta_{z} \), we can apply the identity \( \cos 2\theta = 2\cos^2 \theta - 1 \). By substituting, you might notice that this gives you a relationship tied back to the properties of the direction cosines and leads us to conclude that the answer is \( \mathbf{c) \, 1} \).