Math CentralQuandaries & Queries


Question from Arthi:

Hello. hope you are having a good day.

I am stuck on a maths question in which it is asking, how to find the angle between two given planes. These planes are in a 3D shape such as a prism.
How can I do this?
Please reply as soon as possible

Thank You

Hi Arthi,

I can be very specific without seeing the actual problem but I can give you an idea. The normal way to determine the angle between two planes is to construct a normal to each plane and then calculate the angle between the normals. This is equal to the angle between the planes. If you can work with vectors and $u$ and $v$ are normal vectors to the planes then

\[u \cdot v = |u| \times |v| \times \cos(\theta)\]

where $\theta$ is the measure of the angles between the vectors. Hence if you know $u$ and $v$ you can use the inverse cosine function to find $\theta.$

I hope this is of some help,

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