UnitVector.md (895B)
1 # Unit Vector (Normalized Vector) 2 3 Khan 4 5 **Definition:** A unit vector is any vector with length of 1. 6 7 It is true that ||u|| = 1 when u is a unit vector, in all cases. 8 9 Additionally, it is common practice to add a hat to unit vectors. As such, a hatted vector implies length of 1. 10 11 Commonly we use ihat, jhat, and khat in 3d space where they are each orthogonal and denote some interesting information like right, forward, and up either relative to some object or in global space. 12 13 ## Construction 14 15 To construct a unit vector from any other vector (with same direction) do the following: 16 17 1. Find length of v (sqrt(x_1^2 + x_2^2 + ... + x_n^2)) 18 2. Multiply each component by one over the length of v 19 20 Example (sorry for formatting but not worth my time): 21 22 [4] 23 [7] = u 24 [9] 25 26 ||u|| = sqrt(16 + 49 + 81) 27 = sqrt(146) 28 = 12.083 29 30 [4] [.331] 31 [7] x (1/12.083) = [.579] 32 [9] [.745] 33 34 = $\hat u$