Q. 25

# Write the angle between the line

and the plane x + y + 4 = 0.

Answer :

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

Rate this question :

If lines and intersect, then find the value of k and hence find the equation of the plane containing these lines.

Mathematics - Board PapersFind the coordinates of the point where the line through the points A(3, 4, 1) and B(5, 1, 6) crosses the XZ plane. Also find the angle which this line makes with the XZ plane.

Mathematics - Board PapersState True or False for the statements

The angle between the lineand the plane is .

Mathematics - ExemplarThe sine of the angle between the straight lineand the plane 2x – 2y + z = 5 is

Mathematics - ExemplarThe plane 2x – 3y + 6z – 11 = 0 makes an angle sin^{–1}(α) with x-axis. The valueof α is equal to

Mark against the correct answer in each of the following:

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RS Aggarwal - Mathematics

Mark against the correct answer in each of the following:

The angle between the line and the plane is

RS Aggarwal - Mathematics