Q1 of 230 Page 30

Find the angle between the line and the plane

Equation of line is

_{And the equation of the plane is}

As we know that the angle θ between the line and a plane a₂x + b₂y + c₂z + d₂ = 0 is given by

Here, a₁ = 1, b₁ = 1 and c₁ = 1

and a₂ = 2, b₂ = 3 and c₂ = 4

_{The angle between them is given by}

Find the equation of the plane mid–parallel to the planes 2x – 2y + z + 3 = 0 and 2x – 2y + z + 9 = 0.

Find the distance between the planes and + 7 = 0.

Find the angle between the line and the plane 2x + y – z = 4.

Find the angle between the line joining the points (3, – 4, – 2) and (12, 2, 0) and the plane 3x – y + z = 1.