Q. 25

# Write the angle between the line and the plane x + y + 4 = 0.

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.

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

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