The angle between the lines with direction ratios 1, 1, 2 and (√3−1), (−√3−1), 4 is:

The angle between the lines with direction ratios 1, 1, 2 and (√3−1), (−√3−1), 4 is:

• A. 30°
• B. 45°
• C. 60°
• D. 90°

Answer: C) 60°

Explanation: cos θ = |(1)(√3−1) + (1)(−√3−1) + 2(4)| / [√(1+1+4) * √((√3−1)² + (−√3−1)² + 16)]. Numerator = √3 − 1 − √3 − 1 + 8 = 6. Denominator = √6 * √(4+4+16) = √6 * √24 = √144 = 12. cos θ = 6/12 = 1/2. θ = 60°.