Given :

Equation of line :

Equation of plane : x + y + 4 = 0

To Find : angle between line and plane

Formulae :

1) Parallel vector to the line :

If equation of the line is then,

Vector parallel to the line is given by,

2) Normal vector to the plane :

If equation of the plane is ax + by + cz = d then,

Vector normal to the plane is given by,

3) Angle between a line and a plane :

If Ө is a angle between the line and the plane , then

Where, is vector parallel to the line and

is the vector normal to the plane.

Answer :

For given equation of line,

Parallel vector to the line is

For given equation of plane,

x + y + 4 = 0

normal vector to the plane is

Therefore, angle between given line and plane is