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The angle between the line x - 2 1 = y - 3 2 = z - 4 - 1 and the plane x + y + z = 4 is

Options

  1. Asin -1 2 3
  2. Bcos -1 2 3
  3. Ctan -1 2 1 3
  4. Dtan -1 1 3 2

Correct answer

A. sin -1 2 3

Step-by-step solution

Angle θ between line x - x 1 a = y - y 1 b = z - z 1 c and the plane l x + m y + n z - d = 0 is θ = sin - 1 a l + a m + a n a 2 + b 2 + c 2 l 2 + m 2 + n 2 Here we have line x - 2 1 = y - 3 2 = z - 4 - 1 and plane x + y + z - 4 = 0 So, θ = sin   - 1 1 × 1 + 2 × 1 - 1 × 1 1 2 + 2 2 + - 1 2 1 2 + 1 2 + 1 2 = sin - 1 2 6 × 3 = sin - 1 2 18 = sin - 1 2 3

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