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 – 2

**j**= (0, – 2) and also we have actually

**v**= 3

**i**– 2

**j**. 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**– 3

**j**+4

**k**. 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? | ||