You are watching: How to find a unit vector in the same direction

Introduction: In this lesson, unit vectors and also their an easy components will be defined and also quantified. Us will research both 2- and also 3-dimensional vectors. The Lesson: A unit vector is a vector which has a size of 1. because that example, the vector v = (1, 3) is not a unit vector because
. The notation
represents the norm, or magnitude, the vector v. yet the vector w =
is a unit vector since
. The an easy unit vectors space i = (1, 0) and j = (0, 1) which are of size 1 and have directions along the confident x-axis and also y-axis respectively. To uncover a unit vector with the same direction as a given vector, we divide by the size of the vector. Because that example, take into consideration the vector v = (1, 3) which has a magnitude of
. If we divide each ingredient of v through
we will acquire the unit vector uv i m sorry is in the exact same direction as v:
. Let"s Practice: We very first calculate
. We division each ingredient of r by
and also we have:
We usage scalar multiplication due to the fact that 3i = (3, 0) and also – 2j = (0, – 2) and also we have actually v = 3i – 2j. In three dimensions, we have i = (1, 0, 0), j = (0, 1, 0) and also k = (0, 0, 1) wherein each of these vectors is a unit vector pointing in the direction of the optimistic x-, y-, and also z-axes respectively. together in example (ii), we have v = i – 3j +4k. To discover a unit vector through the exact same direction as v we first calculate
.

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Therefore we have

If vector v = (3, – 7) what is a unit vector through the exact same direction together v?What is your answer?
 Vector w = (2, 4, – 1). Rewrite w together a mix of the an easy vectors i, j, and k. What is a unit vector through the exact same direction together w? What is your answer?