Question

Explain vector with the help of examples.

Answer 1

Vectors:

1. There are quantities in science characterized by both magnitude and direction, such as displacement, velocity, force, and acceleration.
2. To describe such quantities, we introduce the concept of a vector as a directed line segment $\overrightarrow{PQ}$ from one point $P$ to another point $Q$.
3. Here $P$ is called the initial point or origin of $\overrightarrow{PQ}$, and $Q$ is called the terminal point, end, or terminus of the vector.
4. We denote a vector quantity by letters with an arrow over them.
5. The magnitude or length of the vector is then denoted by $\left|\overrightarrow{PQ}\right|$.
6. Two vectors are equal if they have the same magnitude and direction regardless of their initial points.
7. 
8. A vector having a direction opposite to that of a given vector $\overrightarrow{A}$ but having the same magnitude is denoted by $\overrightarrow{-A}$.