Question

What is the difference between collinear and coplanar?

Answer 1

We first discuss the attributes of being collinear and coplanar for points and vectors. Then we define the terms individually. We also express them in their mathematical form to give the relation.

Complete step by step solution:
The given terms ‘collinear’ and ‘coplanar’ are attributes which can be used for different types of cases whether we use points or vectors.
Now we separately discuss the two terms.
Those things can be termed as collinear which consist of one line. It can be for both points and vectors and they are collinear points and collinear vectors.
Collinear points lie on a single straight line. Also, collinear vectors can be represented as the scalar multiple of one another. If $\overrightarrow{p},\overrightarrow{q}$ are two collinear vectors then $\overrightarrow{p}=k\overrightarrow{q}$ where $k$ is a scalar number.
Now we discuss coplanar where things can be termed as coplanar which are situated on the same plane. It can be for both points and vectors and they are coplanar points and coplanar vectors.
Coplanar points lie on a single plane. Also, coplanar vectors can be represented as the linear combination of one another. If $\overrightarrow{p},\overrightarrow{q},\overrightarrow{r}$ are three coplanar vectors then $\overrightarrow{p}=m\overrightarrow{q}+n\overrightarrow{r}$ where $m,n$ are scalar numbers.

Note: We have to remember that the condition of collinear and coplanar can happen in a single case. The characteristics of being coplanar doesn’t guarantee collinearity and vice-versa.