Question

Please Help!
Find the angle between the given vectors to the nearest tenth of a degree.

u = <2, -4>, v = <3, -8>

Answer 1

@satellite73 can you help?

Answer 2

@Hero @phi ?

Answer 3

do you know about "dot product" ?

Answer 4

Yes but when i set it up i get a math error on my calculator

Answer 5

unless i am multiplying them wrong or something?

Answer 6

Forget the calculator for the moment.
the dot product is defined two different ways:
for
\[ a= <a_x, a_y> \] and the same for b
\[ a \cdot b = a_x b_x + a_y b_y \]
also
\[ a \cdot b = |a| |b| cos A\]
where |a| is the "length" of a. same for b. A is the angle between the vectors a and b

Answer 7

right so when i did that i got

Answer 8

use the first definition to find \( a\cdot b\)
use the 2nd definition to find
\[ \cos A = \frac{a\cdot b}{|a| |b| } \]

Answer 9

right so when i did that i got \[38\div \sqrt{20} \sqrt{73}\]

Answer 10

I know its wrong but i dont get what i did incorrectly

Answer 11

so you have
\[ \cos A = \frac{38}{ \sqrt{20 \cdot 73} } \]
(same as what you posted)

Answer 12

Correct...

Answer 13

Oh then i multiply them out! I thought i had to add the square roots. That gives me a final angle of 6 degrees right?

Answer 14

yes. I get 6.0090
to the nearest tenth of a degree, that is 6.0 degrees

Answer 15

Thank you so much!