Unit Vector Calculator
Find the unit vector for any given 2D or 3D vector. This tool helps you normalize vectors quickly, making complex calculations simpler for physics, engineering, and advanced math problems.
Enter the X-coordinate of your vector.
Enter the Y-coordinate of your vector.
Enter the Z-coordinate for 3D vectors. Leave blank for 2D.
Find the unit vector for any given 2D or 3D vector. This tool helps you normalize vectors quickly, making complex calculations simpler for physics, engineering, and advanced math problems.
u = v / ||v|| Where: u = Unit Vector v = Original Vector ||v|| = Magnitude of Vector v
Let's find the unit vector for `v = <3, 4>`. 1. Calculate the magnitude: `||v|| = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5` 2. Divide each component by the magnitude: `û = <3/5, 4/5> = <0.6, 0.8>` The unit vector is `<0.6, 0.8>`. Its magnitude is `sqrt(0.6^2 + 0.8^2) = sqrt(0.36 + 0.64) = sqrt(1) = 1`.
Unit vectors are used to represent direction without magnitude. They are essential in physics for describing forces, velocities, and fields, and in computer graphics for lighting and normal calculations. They simplify vector operations by isolating direction.
Yes, a unit vector can have negative components. The signs of the components simply indicate the direction along each axis. For example, a unit vector pointing directly left would be <-1, 0>. As long as the overall magnitude (length) of the vector is 1, it's a valid unit vector.
Absolutely! Our calculator handles both 2D vectors (by leaving the Z component blank or entering 0) and 3D vectors. Just input the components you have, and it will compute the correct unit vector for your needs.
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