Q22 of 230 Page 30

Find the angle between the line and the plane 10x + 2y – 11z = 3.

Direction ratios of the line are (2,3,6)

Direction ratio of a line perpendicular to the plane

10x + 2y – 11z = 3 are 10, 2, – 11

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

If θ is the angle between the line and the plane, then

∴

⇒

⇒ sinθ = ⇒ θ = sin ^{– 1}(

∴ the angle between the plane and the line is sin ^{– 1}(

Find the coordinates of the point where the line intersects the plane x – y + z – 5 = 0. Also find the angle between the line and the plane.

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane

Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes and

Find the value of k such that the line is perpendicular to the plane 3x – y – 2z = 7.