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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
![A-Level Maths: J2-07 [Vectors: Finding the Angle between Two Vectors]](https://i.ytimg.com/vi/zZ9JzhxhmWo/mqdefault.jpg)
