Statement 1: If θ denotes the angle between the line (x-2)/2=(y-1)/(-3)=(z+2)/(-2) and the plane x+y-z=5, then θ=sin⁻¹(1/√(51)).
Statement 2: The angle made by a line with a plane is the complementary angle of the angle between that line and the normal to the plane.

Question

Accepted Answer

Statement 1 is true, Statement 2 is true, and Statement 2 correctly explains Statement 1. Line direction (2,-3,-2), plane normal (1,1,-1): sin(theta)=|2-3+2|/(sqrt(17)*sqrt(3))=1/sqrt(51), so Statement 1 is true. Statement 2 (line-plane angle is complement of line-normal angle) is true and correctly explains Statement 1.

Statement 1: If θ denotes the angle between the line (x-2)/2=(y-1)/(-3)=(z+2)/(-2) and the plane x+y-z=5, then θ=sin⁻¹(1/√(51)). Statement 2: The angle made by a line with a plane is the complementary angle of the angle between that line and the normal to the plane.

Solution

Related JEE Main Maths questions