Find the angle between the line and the plane 3x + 4y + z + 5 = 0.

Given - and

To find – The angle between the line and the plane

Direction ratios of the line = (3, - 1, 2)

Direction ratios of the normal of the plane = (3, 4, 1)

Formula to be used – If (a, b, c) be the direction ratios of a line and (a’, b’, c’) be the direction ratios of the normal to the plane, then, the angle between the two is given by

The angle between the line and the plane