The angle between the line (x+1)/2 = y/3 = (z−3)/6 and the plane 10x + 2y − 11z = 3 is:

The angle between the line (x+1)/2 = y/3 = (z−3)/6 and the plane 10x + 2y − 11z = 3 is:

• A. sin⁻¹(8/21)
• B. cos⁻¹(8/21)
• C. sin⁻¹(1/21)
• D. cos⁻¹(2/7)

Answer: A) sin⁻¹(8/21)

Explanation: Line DRs: 2, 3, 6 (mag = 7). Plane normal DRs: 10, 2, −11 (mag = √225 = 15). sin θ = |(2)(10) + (3)(2) + (6)(−11)| / (7 * 15) = |20 + 6 − 66| / 105 = 40 / 105 = 8 / 21. θ = sin⁻¹(8/21).