Question

4. Determine the angle between the vectors, given that |u| |v| cos(theta) =u*v

Answer 1

the (6,3) is for the 2nd vector

Answer 2

\[ \theta = \arccos \left( u \cdot v \over ||u|| \; ||v||\right)\]

Answer 3

@Spacelimbus I done another question to de-clutter.

Answer 4

\[ u = (x_2-x_1, y_2-y_1)\]

Answer 5

vector 1 is 5.39
vector 2 is 4.12

Answer 6

using pythag. theorem.

Answer 7

plug everything back into the equation that @experimentX posted above and you're done, you already calculated the numerator in the previous exercise, now you have the length/magnitude of the vectors, thats all you need

Answer 8

I was thinking I was going to need to do a trig function to get the angle. ok.

Answer 9

well, duh, cos.

Answer 10

well, invcos.

Answer 11

is the answer ~0.89?

Answer 12

invcos(14/(5.39)(4.12) ???

Answer 13

in degrees?

Answer 14

My calc is in radians, and thats what she said.

Answer 15

yes but I recommend you working with the exact numbers.

Answer 16

but this way its right

Answer 17

oh, I should not have rounded my answers from c^2? ok. Thanks!!!!!!!!!!!!!!!!!!


So anytime you use dot product (when do you know you need to) you use in arccos and not arctan?

Answer 18

yes because of the definition of the dot product, you need to remember that definition well, it has a trigonometric function embedded to it, therefore also an angle, if you search the angle, you need to use that trigonometric function that is in the formula. In case of the dot product that's the cos function.

Answer 19

When do you know to use dot product? Thank again.

Answer 20

When they ask for angles
Or if two vectors are normal to each other
Or maybe an engineer would use it to see from which direction and vector comes, relative to a line/plane. But now I am leaving my comfort zone (x

Answer 21

God bless.

Answer 22

in highschool/college it's 90% the first case :D