Question

Consider the vector v=(-6, 13).
Part 1: Use the dot product to find the angle (in degrees) between v=(-6, 13) and the vector (1,0). i think the answer is -6

Part 2: Write v in the form (absolutevalueof v costheta, absolutevalueof v sintheta) Express the angle theta in degrees.

Answer 1

If u and v are two vectors, then the formula you want to use to get the angle in between them is:\[u\cdot v=|u||v|\cos\theta\Longrightarrow \cos \theta = \frac{u\cdot v}{|u||v|}\]It seems you got the dot product part, the dot product of the two vectors is -6. All that remains is to get the lengths of the two vectors so you can solve for the angle.

Answer 2

@joemath314159 so is part 1 undefined
and how do i find length....

Answer 3

To find the length of a vector, you treat it like a right triangle. If the vector u is:\[u=(x,y)\]then the length is:\[|u|=\sqrt{x^2+y^2}\]

Answer 4

@joemath314159 so costheta=1?

Answer 5

the length will be a number

Answer 6

if my vector was <2,2> the answer would be sqrt(2^2+2^2) = sqrt(8) = 2sqrt(2)

Answer 7

ok so vector v is sqrt 205 and vector u is sqrt 1? @zzr0ck3r

Answer 8

yes

Answer 9

you can find the angle with tan inverse

Answer 10

so tan inverse(sqrt205)(sqrt1) @zzr0ck3r