LENGTH OF A VECTOR
Definition Of Length Of A Vector
Length of a Vector is nothing but the magnitude of a vector. The length of a vector v is given by| V |.
More About Length of a Vector
Length or magnitude of a vector can never be negative.
In two-dimensional vector space, we can find the length of a vector by using the Pythagorean rule.
In two-dimensional vector space, the length of the vector v = is given as 
In three-dimensional vector space, the length of the vector v = is given as
.
Video Examples: Maths - Measurement Length
Example of Length of a Vector
Length of a vector v = <15, 20=""> =
.
Length of a vector v = <3, 4,="" 6=""> =
Solved Example on Length of a Vector
Ques: Find the length of the vector 
. [Given b = 40 and c = 9.]
Choices:
A. 40
B. 41
C. 45
D. 51
Correct Answer: B
Solution:
Step 1: In â–³OPM, OP = 
[Pythagorean Theorem.]
Step 2: OP =
= 41 [Substitute and simplify.]
Quick Summary
- Length of a vector is its magnitude.
- Magnitude is always non-negative.
- In 2D: |v| = sqrt(x^2 + y^2).
- In 3D: |v| = sqrt(x^2 + y^2 + z^2).
🍎 Teacher Insights
Emphasize the connection to the Pythagorean theorem. Use visual aids to demonstrate vectors in 2D and 3D space. Provide ample practice problems with varying levels of difficulty.🎓 Prerequisites
- Basic Algebra
- Pythagorean Theorem
- Coordinate Geometry
- Vector Representation
Check Your Knowledge
Q1: The vector v = <3, 4>. What is the length of v?
Q2: The vector v = <1, 2, 2>. What is the length of v?
Frequently Asked Questions
Q: Can the length of a vector be zero?
A: Yes, only if all components of the vector are zero (the zero vector).
Q: Is the length of a vector a scalar or a vector?
A: The length is a scalar (a single number representing magnitude).