magnitude of a vector


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 = PQ where P = (12, 12) and Q = (- 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 = , 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.]

Related Terms for Magnitude of a Vector

  • Length
  • Magnitude
  • Vector