Finding end point of a segment, given start point and inclination

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Consider a line segment whose start coordinates $(x,y,z)$ are known, and whose inclination $(a_1,b_1,c_1)$ in all $3$ planes is also known. The length of the line segment is known too. How do we find the end point $(x_2,y_2,z_2)$ of the line segment?

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I'm no expert but maybe it can be done by taking $x=x_1+r\cos\theta_1$ , $y=y_1+r\cos\theta_2$ and $z=z_1+r\cos\theta_3$ Where $r$ is the distance and $x_1$,$y_1$,$z_1$ are the start points... And $\theta_1$, $\theta_2$ and $\theta_3$ are the respective inclinations... I'm not sure..