**Definition of Magnitude of a Vector**

- Magnitude of a Vector is the length of the vector.

**More aAbout Magnitude of a Vector**

- The magnitude of a unit vector is 1.
- If
*V*is the vector, we denote the length or magnitude of by*|V*|.

*|V*| = is the formula for finding the magnitude of the vector, where*x*and*y*are the components of the vector .

**Example of Magnitude of a Vector**

- Let = (2, 3) be a vector. Then the magnitude of is |
*R*| =*x, y*> = = = = .

Therefore, is the magnitude of the vector .

**Solved Example on Magnitude of a Vector**

Let

u = PQwhereP= (12, 12) andQ= (- 9, 40). Which of the following is the magnitude of the vector?

Choices:

A. 21

B. 28

C. 49

D. 35

Correct Answer: D

Solution:

Step 1:u = , whereP= (12, 12) andQ= (- 9, 40).

Step 2:The component form of is = <>x_{2}- x_{1}, y_{2}- y_{1}> = <- 9="" -="" 12,="" 40="" -="" 12=""> = < -="" 21,="" 28="">. [Write the component form of.]

Step 3:The magnitude of is |u| = = = 35. [Use the formula to find the magnitude of a vector.]

**Related Terms for Magnitude of a Vector**

- Length
- Magnitude
- Vector