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The angle between two lines with direction cosines $(l_1, m_1, n_1)$ and $(l_2, m_2, n_2)$ satisfies:
A$\tan\theta = l_1 m_2 - l_2 m_1$
B$\cos\theta = l_1 l_2 + m_1 m_2 + n_1 n_2$
C$\sin\theta = l_1 l_2 + m_1 m_2 + n_1 n_2$
D$\cos\theta = l_1 m_2 + l_2 n_1$
Answer & Solution
Correct answer: B. $\cos\theta = l_1 l_2 + m_1 m_2 + n_1 n_2$
Each set of direction cosines $(l, m, n)$ corresponds to a unit vector along the line. The angle $\theta$ between two unit vectors is the dot product:
$\cos\theta = l_1 l_2 + m_1 m_2 + n_1 n_2$.
Consequence: lines are perpendicular iff $l_1 l_2 + m_1 m_2 + n_1 n_2 = 0$. Lines are parallel iff direction cosines are proportional (same up to sign).
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