HSC Science (Electronics) 12th Board ExamMaharashtra State Board
Share
Notifications

View all notifications

Angle Between Two Planes

Login
Create free account


      Forgot password?

definition

The angle between two planes is defined as the angle between their normals Fig,

notes

Observe that if θ is an angle between the two planes, then so is 180 – θ Fig.

If `vec n _1` and `vec n_2` are normals to the planes and θ be the angle between the planes  
`vec r . vec n _1 = d_1` and `vec r . vec n _2 = d_2` . 
Then θ is the angle between the normals to the planes drawn from some common point We have  
cos θ = `|(vec n_1 . vec n_2)/ (|vec n _1| |vec n_2|)|`

Cartesian form 
Let θ be the angle between the planes, 
`A_1x + B_1y +C_1z + D_1 = 0` and `A_2x +B_2y + C_2 z + D_2 = 0`
The direction ratios of the normal to the planes are `A_1, B_1, C_1` and `A_2, B_2, C_2` respectively.
Therefore , cos θ = `|(A_1 A_2 + B_1 B_2 + C_1 C_2)/ (sqrt(A_1^2 + B_1^2 + C_1^2 ) sqrt (A_2^2 + B_2^2 +C_2^2))|`

Video Tutorials

We have provided more than 1 series of video tutorials for some topics to help you get a better understanding of the topic.

Series 1


Series 2


Shaalaa.com | Three Dimensional Geometry Part 6 - The Plane

Shaalaa.com


Next video


Shaalaa.com


Three Dimensional Geometry Part 6 - The Plane [00:34:04]
S
Series 1: playing of 2
1
0%


S
View in app×