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last thing that we'll go through

um then with the angle between two

vectors so jack when you're looking at

two vectors all right we know we want to

find the angle between them we know

we're going to be looking so far at our

formula of cosine of theta equals the

dot product of u times v divided by the

magnitude of u

times the magnitude of v

right

so let's go ahead and find off to the

side what the magnitude of u is what the

magnitude of v is so the magnitude of u

going to be the square root of four

squared plus

three

how did the square root three squared

yes

okay

so we go 16 plus 9 is going to be 25

so that equals 5.

right

then let's do the magnitude of v

magnitude of v is going to be the square

root of 3 squared

plus 5 squared

so we'll have 9 plus 25 is going to be

the square root of 34 right

okay

then let's do the dot product of u times

v

dot product of u times v is going to be

four

times three

plus three

times five

which equals 12 plus 15

which equals 27.

so therefore i have cosine of theta

equals 27

divided by 5 times the square root of

34.

now we look at this and say can we

simplify anything you know to make this

a little bit easier can we simplify the

square root of 34 can we reduce anything

between 25 27 or 5

no really nothing so to find theta i can

say theta

is going to equal

the cosine inverse of 27 over

5 times the square root of 34.

so now i need to figure out what that

value is

so i'll use my handy calculator donated

by a student who had to go to the

restroom

22.2 okay so much for that video enough

uh inverse cosine

now you have 22.21

so therefore you could say theta equals

22.17

degrees

okay

cool

questions no thank you for your loan

all right