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?
Correct Answer: D
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.] ->