UNIT VECTOR
Definition Of Unit Vector
The Unit Vector of a vector v is given as 
where |v| is the magnitude or norm of the vector v.
More About Unit Vector
The magnitude of a unit vector is 1
Dot product of two unit vectors is the cosine of the angle of the angle between them.
Example of Unit Vector
The unit vector in the direction of the vector v =<1, 2=""> can be found in the following way: Magnitude of the vector v =|v| = 
Unit vector in the direction of v is given as
Hence, the unit vector in the direction of v is = 
Video Examples: Unit Vectors
Solved Example on Unit Vector
Ques: Which of the following is the unit vector in the direction of the vector v= <9, 12="">?
Choices:
Correct Answer: A
Solution:
Step 1: v = <9, 12="">.
Step 2: Magnitude of the vector v = |v| = 
= 15 [Use the formula to find the magnitude of v.]
Step 3: Unit vector in the direction of 
[Write the unit vector of v]
Step 4:= (
) <9, 12="">
Step 5: 
Quick Summary
- Magnitude of a unit vector is always 1.
- Used to represent direction.
- Can be found by dividing a vector by its magnitude.
🍎 Teacher Insights
Emphasize the geometric interpretation of dividing by the magnitude. Use examples in 2D and 3D to illustrate the concept. Connect unit vectors to direction cosines.🎓 Prerequisites
- Vectors
- Magnitude of a Vector
- Scalar Multiplication
Check Your Knowledge
Q1: Which of the following is a unit vector in the direction of v = <9, 12>?
Q2: What is the magnitude of the unit vector?
Frequently Asked Questions
Q: How do you find a unit vector?
A: Divide the vector by its magnitude. If v =
Q: What is the magnitude of a unit vector?
A: The magnitude of any unit vector is 1.