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The direction cosines of a line are $l$, $m$, $n$. They satisfy:
A$l^2 + m^2 + n^2 = 1$
B$l \cdot m \cdot n = 1$
C$l + m + n = 1$
D$l^2 + m^2 + n^2 = 0$
Answer & Solution
Correct answer: A. $l^2 + m^2 + n^2 = 1$
Direction cosines are the cosines of the angles that a line makes with the three coordinate axes: $l = \cos\alpha$, $m = \cos\beta$, $n = \cos\gamma$.
Key identity: $l^2 + m^2 + n^2 = \cos^2\alpha + \cos^2\beta + \cos^2\gamma = 1$.
This just says the unit vector along the line has unit length when projected onto the three axes.
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