Question

Trigonometry??? Find the angle between v and w. Round answer to one decimal place, if nec.?

v=-5i+7j,  w=-6i-4j

Answer 1

Hint: Use Cosine Rule & Pythagoras Theorem

Answer 2

@shiraz14 alright so i have the formula cosa= b^2 + c^2 - a^2/2bc, and the pytha theorem, what do i do with it?

Answer 3

use dot product
w.v=||w||||v||cos(x)
x is the angle we are looking for

Answer 4

cosx=w.v/||w||||v||= ?

Answer 5

what is w.v=?
dot product you know how to do it don't you?

Answer 6

no not really

Answer 7

hmm then forget this lol

Answer 8

come on, i only have 2 questions left this, and this is one of them lol

Answer 9

let u=<s,t> w=<m,n>
the dot product of w and v is define as follows:
w.v=sm+tn

Answer 10

in your case s=-5 and t=7
m=-6 and n=-4

Answer 11

alright i see, its pretty much just plugging them in, so which formula are we using? w.v=sm=tn?

Answer 12

just multiply the components and add them up

Answer 13

hmm formula, am i using any formula?
i said definition of dot product was what i mentioned above

Answer 14

ok so (-5)*(-6)+ 7(-4) which is 30+(-28) so 2

Answer 15

so w.v = 2 right?

Answer 16

yes! that's one part
next if finding ||w||
and ||v||
\[||w||=\sqrt{(-6)^2+(-4)^2}=?\]

Answer 17

do the same to find ||V||

Answer 18

ok yeah i remember that, ||W||=sqrt(52) ||V||=sqrt ((-5)^2 + 7^2) = sqrt(74)

Answer 19

then next is multiply those two values you get
after that you w.v/||w||||v||

Answer 20

so it would be 2/(the value of ||w|| ||V||) ?

Answer 21

yes!

Answer 22

ok so 2/(sqrt52) sqrt(74) = 31.01