Question

What is the measure of the angle between v = <4, 0> and w = <6, 1>?

9.5°

16.3°

18.9°

21.4°

Answer 1

\[u.v=|u||v|\cos \theta\]

Answer 2

hint:
we can apply this formula:
\[\Large \cos \theta = \frac{{u \cdot v}}{{\left\| u \right\|\;\left\| v \right\|}} = ...?\]

Answer 3

where \theta is the requested angle

Answer 4

so the answer is C

Answer 5

@Michele_Laino

Answer 6

we have:
\[\cos \theta = \frac{{u \cdot v}}{{\left\| u \right\|\;\left\| v \right\|}} = \frac{{24}}{{25}}\]
so:
\[\theta = \arccos \left( {\frac{{24}}{{25}}} \right) = ...?\]

Answer 7

16.3

Answer 8

but I wonder how you get the 25 at the bottom?

Answer 9

I'm sorry I have made an error, since we can write:
\[\begin{gathered}
\left\| u \right\| = length\;of\;u = 4 \hfill \\
\left\| v \right\| = length\;of\;v = \sqrt {{6^2} + {1^2}} = \sqrt {36 + 1} = \sqrt {37} \hfill \\
\end{gathered} \]

Answer 10

so:
\[\begin{gathered}
\cos \theta = \frac{{u \cdot v}}{{\left\| u \right\|\;\left\| v \right\|}} = \frac{{24}}{{4\sqrt {37} }} \hfill \\
\hfill \\
\theta = \arccos \left( {\frac{{24}}{{4\sqrt {37} }}} \right) = ...? \hfill \\
\end{gathered} \]

Answer 11

sorry again for my error

Answer 12

you straight

Answer 13

hey got it wrong but it is A

Answer 14

yes! it is A

Answer 15

\[\theta = \arccos \left( {\frac{{24}}{{4\sqrt {37} }}} \right) = 9.46\]