Discussion
The direction ratios of a straight line L1 are 2,-1,2 and that of another straight line L2 are 3,6,-2 . Then the angle between L1 and L2 is
Answer: A
The key gives \(\cos^{-1}\left(\frac{-4}{21}\right)\), the angle between the two direction vectors as given.
\[ \begin{aligned} \cos\theta &= \frac{2(3) + (-1)(6) + 2(-2)}{\sqrt{9}\sqrt{49}} \\ &= \frac{6 - 6 - 4}{3 \times 7} = \frac{-4}{21} \end{aligned} \]
The angle between two lines is often quoted as the acute one, \(\cos^{-1}\frac{4}{21}\), but that value is not among the options; the options list only the angle between the direction vectors (2, -1, 2) and (3, 6, -2), which is obtuse. \(\frac{-4}{7}\) leaves out the factor 3 for \(|(2, -1, 2)|\), and the positive fractions come from errors in the dot product.
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