MHB Find Direction Angles: Calculate & Understand

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Direction angles are the angles that a vector makes with each coordinate axis. The length of the vector is calculated as $\sqrt{2 + 4 + 2} = 2\sqrt{2}$. For the x-axis, the length is $\sqrt{2}$, leading to a cosine value of $\frac{1}{2}$. This indicates that the angle with the x-axis can be determined using the inverse cosine function. Similar calculations can be applied to find the angles with the y-axis and z-axis.
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Do you know what "direction angles" are? They are the angles the vector makes with each of the coordinate axes. The length of this vector is $\sqrt{2+ 4+ 2}=\sqrt{8}= 2\sqrt{2}$. That is the length of the hypotenuse of the right triangles the vector makes with each of the axes. The length of the side along the x-axis has length $\sqrt{2}$. The cosine of that angle is $\frac{\sqrt{2}}{2\sqrt{2}}= \frac{1}{2}$. So what is that angle?

Do the other angles the same way.
 

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