Vectors so far

Review of Vectors so far

By KYLA NAULT

Review

I wanted to review everything we have done with vectors so far! That includes

• ​Intro to Vectors

• Component form

• Magnitude

• Adding Vectors

• Direction of Vectors

Intro to Vectors

As a reminder, vectors have two key features! Do you recall what they are?

Multiple Select

What are the two key features of a vector? Select all that apply

• Strength

• Speed

• Magnitude

• Time

• Direction

Intro to vectors (cont)

In case you forgot, vectors have both direction and magnitude.

Also! Quick Refresher over distance and displacement

distance - how far you have traveled in total and is scalar

displacement - how far you are from where you started and is a vector

Component Form

Component form is how we write vectors. It looks like the thing to the right

a is the horizontal component and
b is the vertical component

Component form (cont)

Sometimes you will be given the initial point (the starting point) and the terminal point (the ending point). If given this information, you can calculate the component form of a vector by using the following equation:

Initial Point: Terminal Point:

Component form (cont)

Take into consideration the following points:

Initial Point: Terminal Point:

Multiple Choice

What is the component form of the following vector?

Initial Point: ( -4 , 5 ) Terminal Point: ( 3 , 1 )

• < -7 , 4 >

• < 7 , -4 >

• < -1 , 6 >

• <-4 , 4 >

Magnitude

After component form, we covered Magnitude (which is how long the vector is), To calculate magnitude, is like doing the Pythagorean Theorem:



Where a and b are from the component form of the vector

Magnitude

Example, take the vector < 3 , -4 >

​Reminder: Magnitude is always positive

Multiple Choice

What is the magnitude of the following vector?

$$<-6,8>$$

• 10

• -10

• 2

• 100

Adding Vectors

Personally, I find adding vectors to be pretty chill

All you have to do is the add like components (x's with x's, y's with y's, i's with i's, or j's with j's)

Have a look see on the next slide

Adding Vectors (cont)

Add the following vectors:

​a < 1 , 3 > b <-2 , 5 >
a+b
<(1 + -2) , (3 + 5)>
<-1 , 8>

​c 4i + 7j d -3i + -2j
c + d
(4 + -3)i + (7 + -2)j
i + 5j

Multiple Choice

Add vectors x and y

$$x\ <-8,10>$$ $$y<4,4>$$

• < -12 , 6 >

• < 12 , 14 >

• < 4 , 6 >

• < -4 , 14 >

Direction of Vectors

There are 8 scenarios of finding the direction of a vector and it all comes down to seeing if the values you are given in component form are positive, negative, or a zero. Take a look at this handy guide!
I just posted an IXL yesterday (March 11th) That covers Direction practice. So I will not include any in these slides

Wrap up?

In all honesty, I just wanted to give a quick refresher of how to tackle most everything when it comes to vectors (the only thing left is multiplying them but that will be after spring break)

Hopefully this jogs your memory so far!