Question

Help please! :)
use the dot product to find the angle (in degrees) between v=(-6,13) and the vector (1,0).

Answer 1

So our formula for this is:
\[\cos \theta = \frac{ u*v }{ ||u||*||v|| }\] Of course I mean the numerator to be a dot, but yeah. So now we just need to use the dot product on your two vectors. Do you know how to do that?

Answer 2

not really :/

Answer 3

Well, you have
(-6i, 13j) and (1i, 0j). You need to multiply the i terms and multiply the j terms, then combine them together. Your answer will be a number, so we drop the i and j, I just have them there so you know which terms to multiply.

Answer 4

-6=i and 0=j so do I put these numbers in the formula?

Answer 5

Well, you would then add them, which just gives you -6. So -6 goes in the numerator and we now have:
\[\cos \theta = \frac{ -6 }{ ||u||*||v|| }\]
Now we just need to calculate the magnitudes of u and v. Do you know how to find the magnitude?

Answer 6

it sounds really familiar but I don't know how to find it

Answer 7

Magnitude is the vector terminology for the length of the vector really. So a vector usually is (ai + bj) where i acts like x-coordinates and j acts like y-coordinates. So just for example, let's graph your first vector.

Answer 8

Would you know how to find the length of that?

Answer 9

no lol

Answer 10

Distance formula/pythagorean theorem ^_^