Magnitude of a Vector
Definition of Magnitude of a Vector
Magnitude of a Vector is the length of the vector.
More About 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 .
Examples 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 .
Video Examples: CSEC CXC Maths Finding The Magnitude OF A Vector.
Solved Example on Magnitude of a Vector
Ques: Let u = PQ where P = (12, 12) and Q = ( 9, 40). Which of the following is the magnitude of the vector?
Choices:
A. 21B. 28
C. 49
D. 35
Correct Answer: D
Solution:

Step 1: u = , where P = (12, 12) and Q = ( 9, 40).
Step 2: The component form of is = < x2  x1, y2  y1> = < 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.]
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