What is Unit Vector ?
What is Unit Vector ?
Aniket Singh , 1 Year ago
Grade
11 grade physics others> What is Unit Vector ?...
1 AnswersAskiitians Tutor Team
A unit vector is a vector that has a magnitude (length) of 1. It is often used to represent direction without specifying a particular magnitude. Unit vectors are typically used in vector algebra and physics to indicate direction.
In general, any vector can be converted into a unit vector by dividing the vector by its magnitude. If v is a vector, and |v| is its magnitude, the unit vector v̂ in the direction of v is given by:
v̂ = v / |v|
Where:
v is the original vector.
|v| is the magnitude of vector v.
v̂ is the unit vector in the direction of v.
For example, if a vector v = (3, 4), the magnitude |v| would be calculated as:
|v| = √(3² + 4²) = √(9 + 16) = √25 = 5
Then, the unit vector v̂ would be:
v̂ = (3/5, 4/5)
This gives a vector in the same direction as v, but with a magnitude of 1.
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