Condition for Parallel Vectors Using Components

Condition for Parallel Vectors Using Components

If:

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

and:

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

then parallelism requires:

$$\frac{a_1}{b_1}=\frac{a_2}{b_2}=\frac{a_3}{b_3}$$

where the relevant denominators are non-zero.

Usage

- Used to test parallelism using Cartesian components.