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Mathematical Investigations IV Name: Vectors Getting To the Point Unit Vectors Given a vector v we know how to find its magnitude |v|. We know how to find the angle that v makes when measured from the positive x-axis, or when measured as a bearing from reference direction north in a navigational context. Summarize these here for a vector v = <a, b>. Give formulas in terms of a and b, assuming the vector is in the first quadrant as shown. |v| = (a, b) angle with respect to the positive x-axis = bearing from due north = There is another way to describe the direction of a v called the unit vector in the v-direction. The unit vector has a magnitude of 1 (hence the name “unit” vector) and points in the same direction as v. You may remember that we have defined iˆ = unit vector in the positive x direction = <1, 0> ĵ = unit vector in the positive y direction = <0, 1> (watch the symbols carefully!) The unit vector in the direction of v is often denoted by the symbol v̂ and is defined as vˆ v v Note that this implies that v | v | vˆ for any vector v . Vectors 4.1 Rev. F08 Mathematical Investigations IV Name: 1. Every non-zero vector has a unit vector associated with it. Find the unit vectors associated with the following vectors: w w ŵ <3, –4> 5 3 4 , 5 5 <1,1> 3 1 5iˆ 12 ĵ cos iˆ sin ĵ <x, y> Vectors 4.2 Rev. F08