If the direction ratios of two lines are (1, 2, 3) and (-2, 3, -4), Then the angle between the lines is:

Correct option is D

​$$\text{Formula:} \\\text{The angle } \theta \text{ between two vectors is given by:} \\\cos \theta = \frac{\mathbf{a} \cdot \mathbf{b}}{|\mathbf{a}| \cdot |\mathbf{b}|} \\\textbf{Dot product } \mathbf{a} \cdot \mathbf{b} \\\mathbf{a} \cdot \mathbf{b} = (1)(-2) + (2)(3) + (3)(-4) = -2 + 6 - 12 = -8 \\\textbf{Magnitudes} \\|\mathbf{a}| = \sqrt{1^2 + 2^2 + 3^2} = \sqrt{1 + 4 + 9} = \sqrt{14} \\|\mathbf{b}| = \sqrt{(-2)^2 + 3^2 + (-4)^2} = \sqrt{4 + 9 + 16} = \sqrt{29} \\\textbf{Compute } \cos \theta \\\cos \theta = \frac{-8}{\sqrt{14} \cdot \sqrt{29}} = \frac{-8}{\sqrt{406}}$$​​