Question

Use the formula v1 x v2 = absltvalue v1 x absltvalue v2 to find the cosine of the angle between the two vectors (-7,8) and (1,0).

Answer 1

hi!!

Answer 2

you got the length of each of these?

Answer 3

dot product should be easy since because of the \((1,0)\) it is just \(-7\)

Answer 4

So Im just curious in the equation when it says multiply v1 by v2 does that mean you multiply the x and y values of (-7,8) and (1,0) together and than add the x and y values together?

Answer 5

^^ yes
\[v_1*v_2 = (x_1,y_1) * (x_2,y_2) = x_1 *x_2 + y_1*y_2\]

Answer 6

so the equation would come out to be -7=7costheta. Which would then simplify down to -1=costheta. Then you solve for theta giving you 180 degrees?

Answer 7

@dumbcow

Answer 8

equation is
\[\cos \theta = \frac{v_1 *v_2}{|v_1| |v_2|}\]
\[\cos \theta = \frac{-7}{\sqrt{113}}\]
\[\theta \approx 131.2\]