The angle between two planes is defined as:

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The angle between two planes is defined as the angle between their normal vectors. If the equations of the two planes are $a_1x + b_1y + c_1z + d_

Vedclass · Accepted Answer

The angle between the normals to them from any point

Vedclass · Answer

(B) The angle between two planes is defined as the angle between their normal vectors. If the equations of the two planes are $a_1x + b_1y + c_1z + d_1 = 0$ and $a_2x + b_2y + c_2z + d_2 = 0$,their normals are $\vec{n_1} = a_1\hat{i} + b_1\hat{j} + c_1\hat{k}$ and $\vec{n_2} = a_2\hat{i} + b_2\hat{j} + c_2\hat{k}$. The angle $	heta$ between the planes is given by $\cos 	heta = \frac{|\vec{n_1} \cdot \vec{n_2}|}{|\vec{n_1}| |\vec{n_2}|}$.

Similar Questions

The vector equation of a plane,which is at a distance of $8$ units from the origin and which is normal to the vector $\vec{n} = 2\hat{i} + \hat{j} + 2\hat{k}$,is

The equation of the plane passing through the point $(-1, 2, 1)$ and perpendicular to the line joining the points $(-3, 1, 2)$ and $(2, 3, 4)$ is $.........$

Find the equation of the plane that contains the point $(1, -1, 2)$ and is perpendicular to each of the planes $2x + 3y - 2z = 5$ and $x + 2y - 3z = 8$.

Equation of planes parallel to the plane $x-2y+2z+4=0$ which are at a distance of one unit from the point $(1,2,3)$ are

Find the equation of the plane passing through the intersection of the planes $3x - y + 2z - 4 = 0$ and $x + y + z - 2 = 0$ and the point $(2, 2, 1)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module