Statement 1 - Let θ be the angle between the line 2 x − 2 = − 3 y − 1 = − 2 z + 2 and the plane x + y − z = 5 . Then θ = sin − 1 51 1 . Statement 2 - The angle between a straight line and a

Question

Statement 1 - Let θ be the angle between the line 2 x − 2 ​ = − 3 y − 1 ​ = − 2 z + 2 ​ and the plane x + y − z = 5 . Then θ = sin − 1 51 ​ 1 ​ . Statement 2 - The angle between a straight line and a plane is the complement of the angle between the line and the normal to the plane.

TestHub · Accepted Answer

sin θ = 4 + 9 + 4 ​ 3 ​ ∣2 ⋅ 1 − 3 ⋅ 1 + ( − 2 ) ( − 1 ) ∣ ​ = 51 ​ 1 ​ . Statement 1 is true. Statement 2 is true and it is the reason for using sin θ = ∣ d ∣∣ n ∣ ∣ d ⋅ n ∣ ​ , so it explains Statement 1.

Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

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