You are watching: Find the unit vector having the same direction as v

**Introduction:**In this lesson, unit vectors and also their simple components will be defined and quantified. We 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 due to the fact that . The notation represents the norm, or magnitude, of vector

**v**. yet the vector w = is a unit vector since . The simple unit vectors room

**i**= (1, 0) and also

**j**= (0, 1) which space of length 1 and have directions follow me the positive x-axis and y-axis respectively. To discover a unit vector through the same direction together a provided vector, we divide by the size of the vector. For example, take into consideration the vector

**v**= (1, 3) which has a magnitude of . If we divide each component of

**v**by us will gain the unit vector

**uv**which is in the exact same direction as

**v**: .

**Let"s Practice:**We very first calculate . We division each ingredient of

**r**through and we have: We use scalar multiplication because

**3i**= (3, 0) and also – 2

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

**v**= 3

**i**– 2

**j**. In 3 dimensions, we have

**i**= (1, 0, 0),

**j**= (0, 1, 0) and

**k**= (0, 0, 1) wherein each of these vectors is a unit vector pointing in the direction that the hopeful x-, y-, and z-axes respectively. as in instance (ii), we have actually

**v**=

**i**– 3

**j**+4

**k**. To discover a unit vector with the very same direction together

**v**we very first calculate .

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As such we have actually

If vector

**v**= (3, – 7) what is a unit vector v the exact same direction as

**v**?What is her answer?

Vector w = (2, 4, – 1). Rewrite w together a mix of the straightforward vectors i, j, and k. What is a unit vector with the very same direction as w? | ||

What is your answer? | ||