Angle Between Two Vectors Using Components

Angle Between Two Vectors Using Components

For:

$$\vec a=a_1\hat i+a_2\hat j+a_3\hat k$$

and:

$$\vec b=b_1\hat i+b_2\hat j+b_3\hat k$$

the angle satisfies:

$$\cos\theta=\frac{a_1b_1+a_2b_2+a_3b_3}{\sqrt{a_1^2+a_2^2+a_3^2}\sqrt{b_1^2+b_2^2+b_3^2}}$$

Usage

- Used to find the angle directly from Cartesian components.