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I am preparing for my calculus III class over the break. I came across the formula for the angle between two planes which is:

cosΘ = (|a.b|)/(||a|||b||)

I know that the dot product formula is:

a.b = ||a||||b||cosΘ

Why do we put the absolute value bars when we are trying to find the angle between two planes if the original formula doesn't have absolute values in it?

## Homework Statement

I am preparing for my calculus III class over the break. I came across the formula for the angle between two planes which is:

cosΘ = (|a.b|)/(||a|||b||)

cosΘ = (|a.b|)/(||a|||b||)

a.b = ||a||||b||cosΘ## Homework Equations

cosΘ = (|a.b|)/(||a|||b||)

a.b = ||a||||b||cosΘ

## The Attempt at a Solution

I know that the dot product formula is:

a.b = ||a||||b||cosΘ

Why do we put the absolute value bars when we are trying to find the angle between two planes if the original formula doesn't have absolute values in it?