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As shown in the figure, the direction cosines represent the cosines of the angles made between the vector and the three coordinate directions.
The direction cosines of a nonzero vector v = AXi + AYj + AZk
cos α = AX/||v||cos β = AY/||v||cos γ= AZ/||v||
where the angles α, β, and γ are the angles shown in the figure.
a. Show that: cos2 α + cos2 β + cos2 γ = 1.
b. Find the direction cosines of the vector v = 2i - 4j + 4k. and approximate the direction angle to the nearest degree.
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