# Vectors

###### Sections

- Vectors
- Resultant displacement
- Force vector
- Multiplication of a vector by a number
- Subtraction of vectors
- Unit vectors
- Components of a vector

##### Multiplication of a vector by a number

The drawing below explains it.

Figure 9

**Q**. Can you get a vector pointing in some other direction by multiplying a vector by a number?

**A**. Multiplication by a number can only give you a vector either in the same direction (the number is positive) or a vector in the opposite direction (if the number is negative). Or a zero vector if you multiply by zero. The zero vector has no direction. You can never get a non-zero vector in another direction.

If you had to solve the equation y**a** = x**b** , given that **b** is in a direction different from that of **a**, the only solution is x = y = 0.

Notice that defining the negative of a vector as a vector of the same length pointing in the opposite direction is consistent with adding the two to get zero: **a** + (-**a**) = 0.