Q 7. - Calculus

Question

What does it mean for three points to be collinear? How do you determine that the three given points are collinear? What does it mean for three points to be noncollinear?

Step-by-Step Solution

Answer

The three points are collinear if they are scalar multiple of each other. If the two vectors $\overrightarrow{PR}$ and $\overrightarrow{PO}$ are parallel, they must be collinear.

The points are said to be noncollinear if the two vectors $\overrightarrow{PR}$ and $\overrightarrow{PQ}$ are not parallel.

Step 1: Given information

The three points $P, Q$ and $R$ to be collinear.

Step 2: Calculation

The goal is to explain what collinear points are and what they imply.

If the points lie on a single line, they are collinear.

The points $P, Q$ and $R$ are collinear. Thus, they lie on a single line.

If the three points are scalar multiples of each other, they are collinear. If the two vectors $\overrightarrow{PR}$ and $\overrightarrow{PQ}$ are parallel, they must be collinear.

Check whether the vectors are parallel or not to see if they are collinear..

Step 3: Calculation

If the three points do not lie on a single line, they are non-collinear. The points are said to be noncollinear if the two vectors $\overrightarrow{PR}$ and $\overrightarrow{PQ}$ are not parallel.