The plane ( 2 x-3 y+6 z-11=0 ) makes an angle ( ⁻¹( ) ) with ( X )-axis. The value of a is equal to

Step-by-step solution

Given plane, ( u: 2 x-3 y+6 z-11=0 (1) ) Equation of plane on x-axis is given by ( v: 1 x+0 y+0 z=0 (2) ) Angle between two planes is given by [ array l = |u v| |u| |v| = |(2) (1)+(-3) (0)+(6) (0)| 2²+3²+6² 1² = 2 49 = 2 7 = ⁻¹ ( 2 7 ) array ] Since, ( ⁻¹ = ). Then, ( ⁻¹ = ⁻¹ ( 2 7 ) = 2 7 )