Unit Vector
A unit vector is a vector that has a magnitude of 1
A unit vector is a vector that has a magnitude of 1. In other words, it is a vector that has been normalized such that its length or magnitude is equal to 1. Unit vectors are commonly used in mathematics and physics to represent direction.
To find the unit vector of a given vector, you need to divide the vector by its magnitude. The magnitude of a vector can be found using the Pythagorean theorem or the Euclidean norm. Once you have the magnitude, divide each component of the vector by the magnitude to obtain its normalized form.
For example, let’s say we have a vector v = (3, -4). To find the unit vector u in the same direction, we first find the magnitude of v:
|v| = sqrt(3^2 + (-4)^2) = sqrt(9 + 16) = sqrt(25) = 5
Now we divide each component of v by its magnitude:
u = (3/5, -4/5)
The resulting vector (3/5, -4/5) is the unit vector in the same direction as the original vector (3, -4).
Unit vectors have many applications, such as representing the direction of forces in physics, specifying directions in 3D graphics, or representing directions in geometric problems.
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