# Find Unit Vector Parallel to Vector: (5,1,-3) to (2,1,1)

• mamma_mia66
In summary, the conversation is about finding a unit vector that is parallel to the vector between the points (5,1,-3) and (2,1,1). The suggested solution is to first find a vector that goes between the two points, and then scale it correctly to get the desired unit vector. The difference between any old vector and a unit vector is the scaling factor, which can be found by dividing the original vector by its magnitude. The final solution is to use the formula u=c.v, where u is the desired unit vector, v is the vector between the two points, and c is the scaling factor.
mamma_mia66

## Homework Statement

Find a unit vector that is parallel to the vector from )5,1,-3) to (2,1,1)

## The Attempt at a Solution

I will appreciate any HINT for this problem b/c I am totaly confused from the why how the question is stated. Please help.

First find a vector that goes between those 2 points

Well, you know what the direction of the vector is, you just have to scale it correctly...

Well, you know what the direction of the vector is, you just have to scale it correctly...

I don't think I get this that I have to scale it correctly...

mamma_mia66 said:
Well, you know what the direction of the vector is, you just have to scale it correctly...

I don't think I get this that I have to scale it correctly...

What's the difference between any old vector and unit vector?

okay, I am following the textbook and nothings helps.

The points (5,1,-3) and (2,1,1) are the points of the vector V=<-3,0,4>

Then ||v||= 5
u= v/||v||= 1/5<-3,0,4>
Two nonzero vectors u avd v are parallel if there is some scalar c
such that
u=c.v

Am I even close with this solution? I am getting more confused.

That's the vector you want.

Thank you.

## 1. What is a unit vector?

A unit vector is a vector that has a magnitude of 1 and points in a specific direction. It is commonly used in mathematics and physics to represent the direction of a vector without considering its magnitude.

## 2. How do you find the magnitude of a vector?

The magnitude of a vector is equal to the square root of the sum of the squares of its components. In this case, the magnitude of the given vector is √(5² + 1² + (-3)²) = √35.

## 3. What does it mean for two vectors to be parallel?

Two vectors are parallel if they have the same or opposite direction. In other words, their direction vectors are scalar multiples of each other. Geometrically, parallel vectors lie on the same line or are parallel to each other.

## 4. How do you find a unit vector parallel to a given vector?

To find a unit vector parallel to a given vector, you first need to find the magnitude of the vector. Then, divide each component of the vector by its magnitude. The resulting vector will have a magnitude of 1 and will be parallel to the given vector.

## 5. Can a vector have more than one unit vector parallel to it?

Yes, a vector can have an infinite number of unit vectors parallel to it. This is because you can multiply the unit vector by any non-zero scalar and still get a vector with a magnitude of 1 and parallel to the given vector.

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