Question

estimate the angle between the two vectors <-2, 1> and <2,4>

Answer 1

Are you familiar with this formula?

a⋅b = |a||b|cosθ

Answer 2

no, can you please help

Answer 3

hmm, best way to estimate is to plot vector, where both vector start from same point, then guess angle from there.

Answer 4

Best approach I can think of...

Answer 5

\(\bf \textit{angle between two vectors }\\ \quad \\
cos(\theta)=\cfrac{u \cdot v}{||u||\ ||v||} \implies \cfrac{\text{dot product}}{\text{product of magnitudes}}\\ \quad \\
\theta = cos^{-1}\left(\cfrac{u \cdot v}{||u||\ ||v||}\right)\)

Answer 6

what is the dot product and product of magnitudes?

Answer 7

is that multiplying both x and adding then multiply both y and adding?

Answer 8

what class are you taking right now?

Answer 9

math analysis

Answer 10

hmmm

Answer 11

huh? is that after algebra 2?

Answer 12

there's an assumption you'd know what a dot product and magnitude are

Answer 13

yes, it it is the equivalent to pre calc

Answer 14

I didn't learn vectors in algebra 2

Answer 15

ah i see, never heard of it being called math analysis haha.

Answer 16

another route is trig

<-2, 1>
tan(a) = -1/2

and <2,4>
tan(b) = 4/2

the difference between a and b is just:

tan(a-b) = tan(a)-tan(b)/(1+tan(a)tan(b))

and invert the trig

Answer 17

thank you, that makes more sense! I'm really trying to understand this, I appreciate your help and patience

Answer 18

hmm, a zero divisor, what does that tell us? same thing as the dot product = 0 really

Answer 19

perpendicular?

Answer 20

yep

Answer 21

which is the same as evaluating slopes:

-1/2 *4/2 = -1 which is of course a property of perp slopes

Answer 22

alright, thanks so much, I get it now!

Answer 23

good luck :)

Answer 24

thanks