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  example of  Magnitude of a Vector |V|.
    •  example of  Magnitude of a Vector
  • |V| =  example of  Magnitude of a Vector 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 .
    •  example of  Magnitude of a Vector

Examples of Magnitude of a Vector

  • Let =  example of  Magnitude of a Vector (2, 3) be a vector. Then the magnitude of  example of  Magnitude of a Vector is |R| = x, y>  example of  Magnitude of a Vector =  example of  Magnitude of a Vector=  example of  Magnitude of a Vector =  example of  Magnitude of a Vector = . Therefore  example of  Magnitude of a Vector, is the magnitude of the vector  example of  Magnitude of a 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 example of  Magnitude of a Vector?

    Choices:
    A. 21
    B. 28
    C. 49
    D. 35
    Correct Answer: D

Solution:

    Step 1: u =  example of  Magnitude of a Vector , where P = (12, 12) and Q = (- 9, 40).
    Step 2: The component form of  example of  Magnitude of a Vector is  example of  Magnitude of a Vector = <>x2 - x1, y2 - y1> = <- 9="" -="" 12,="" 40="" -="" 12=""> = < -="" 21,="" 28="">. [Write the component form of  example of  Magnitude of a Vector.]
    Step 3: The magnitude of  example of  Magnitude of a Vector is |u| =  example of  Magnitude of a Vector =  example of  Magnitude of a Vector= 35. [Use the formula to find the magnitude of a vector.]