Angle Between Lines Using Direction Ratios

Angle Between Lines Using Direction Ratios

If the direction ratios are:

$$a_1:b_1:c_1$$

and:

$$a_2:b_2:c_2$$

then:

$$\cos\theta=\frac{a_1a_2+b_1b_2+c_1c_2}{\sqrt{a_1^2+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2}}$$

Usage

- Used when lines are given through direction ratios instead of direction cosines.