Question

The angle between the lines \[ \frac{x-1}{1} = \frac{y+1}{2} = \frac{z-3}{-1}, \quad \frac{x-1}{2} = \frac{y-3}{3} = \frac{z-1}{4}, \] where \( l, m, n \) are roots of the equation \[ x^2 + x^2 - 4x - 4 = 0, \] is

• A. \( \cos^{-1} \left( \frac{2}{3} \right) \)
• B. \( \cos^{-1} \left( \frac{1}{3} \right) \)
• C. \( \cos^{-1} \left( \frac{3}{4} \right) \)
• D. \( \cos^{-1} \left( \frac{1}{4} \right) \)

Hint:

To find the angle between two lines, use the formula involving the dot product of their direction vectors and their magnitudes.

Answer 1

The Correct Option is A