The angle between a line with direction ratios 2, 1, 2 and a plane with equation x − 2y + 2z = 5 is:

The angle between a line with direction ratios 2, 1, 2 and a plane with equation x − 2y + 2z = 5 is:

• A. cos⁻¹(4/9)
• B. sin⁻¹(4/9)
• C. sin⁻¹(2/9)
• D. cos⁻¹(2/3)

Answer: B) sin⁻¹(4/9)

Explanation: Line DRs: 2, 1, 2 (mag 3). Plane Normal DRs: 1, −2, 2 (mag 3). sin θ = |(2)(1) + (1)(−2) + (2)(2)| / (3 * 3) = |2 − 2 + 4| / 9 = 4/9. θ = sin⁻¹(4/9).