**Position vectors**are vectors that give the position of a point from the origin. The vector is denoted as and starts at point and ends at point .

This brings us to how to find a vector given an initial and final point. Given two points and , the vector , which goes from point A to B, is .

**Adding vectors**is very simple

Given two vectors

Here’s an example of adding vectors (click here):

**Subtracting vectors**is just as simple

Given two vectors

**Scalar multiplication**is used to lengthen or shorten a vector

Given two vectors and any number c,

Here’s an example of scalar multiplication (click here):

Every vector has a magnitude and a direction. The direction is where its arrow is pointed and the magnitude is the length of the vector. If the magnitude of a vector is 1, then we call that vector a unit vector.

**is denoted as or .**

__Magnitude__We will use , so we don't get confused with absolute values.

Here’s an example of finding a vector’s magnitude (click here):

**, is a vector with length 1.**

__A unit vector__Here’s an example of finding the unit vector of a vector (click here):

Here are some properties to memorize about basic vector arithmetic:

The topics we covered in this blog are simple. I recommend practicing a few examples and memorizing the formulas, and you should be good to go. We are going to cover some of the heavier vector topics in next blog.

Until next time,

Leah

On Symbolab if you have purchased it once then you want to download it to your phone why do you have to purchase it again?

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