Vectors 7.3/7.4 The Dot Product (R2)

Two formulas for the dot product for use with geometric and algebraic vectors. How to calculate the angle between two vectors that are tail to tail. How to tell if your vectors are perpendicular (ORTHOGONAL). Properties of the dot product and an example to show how to find an angle given a triangle on a coordinate plane (THINK position vectors FIRST) and how to use the properties of the dot product (see question 11 page 377).

[mshavrotscanadianuniversit]

For your first question you are moving the triangle so that E is at the origin. Therefore you need ED not DE. The second triangle is the repositioned triangle.

[vmplina]

i got into harvard because of your videos. u are my goat🔥

[anna-obwb]

at 22:00, i’m a bit confused how you got -6a • b from the above line. are you allowed to subtract the -a from the -5b even though they have different variables? and how did only a single b result?

[hollowayfan]

Miss for the DEF triangle question
You first found the position vector for ED, but would it matter if you did DE instead?
If it does matter how do you make sure to do the right order

I also don’t understand why you made another triangle using 2 vectors

Also at 22:07 I’m very confused how you got -6a dot b

[maiarusso]

Hi Ms. Havrot! Thank you so much for your videos, they’re extremely helpful!

I’m a little confused about Properties #4 and #5.

For #4, if I want to find 3(vector u • vector v) when vector u = [5, -4] and vector v = [2, 3], is the following process correct?

First I find 3(vector v) which is [3(2), 3(3)] = [6, 9].

Then I find the dot product of [5, -4] and [6, 9] which is (5)(6) + (-4)(9) = -6.

Can you please provide a similar example for Property #5?

[hollowayfan]

Miss for rule 4 at 13:20, what about if each vector has its own constant?

[iangorlick]

I believe there is a fundamental problem with the last example. If a dot b equals 1 and both a and b are unit vectors then cosine theta has to be 1 and theta=0 degrees, that is a and b are identical vectors. That means that (a-b) is the zero vector.
So the statement (a-5b)dot(a-b)=0 does NOT mean the two vectors are orthogonal, it just means one of the factors is a zero vector.

[Monica-bepg]

Hey ms.havrot! Your videos r so helpful! Do you have any example questions about calculating the work and projection of vectors?? My school uses the McGraw hill textbook so the units don’t really match w Nelson :(((

[sakshampujara]

Whats the difference in a cartesian and geometric vector and plane?

[LearnToday]

why F-E?
isn't it vector EF

(15:55)