The angle between the line x - 1 = 2 - y = 2z - 6 4 and the plane r (2 i + j + k ) = 10 is

Step-by-step solution

The equation of the line can be rewritten in standard form as: x - 1 1 = y - 2 -1 = z - 3 2 The direction vector of the line is b = i - j + 2 k . The equation of the plane is r (2 i + j + k ) = 10 . The normal vector to the plane is n = 2 i + j + k . The angle between the line and the plane is given by: = | b n | | b | | n | = |(1)(2) + (-1)(1) + (2)(1)| 1^2 + (-1)^2 + 2^2 2^2 + 1^2 + 1^2 = |2 - 1 + 2| 6 6 = 3 6 = 1 2 = 6 Answer: 6