Question

Find the angle theta between two vectors.
u= 5i + 20j
v= -3i+6k

Answer 1

u dot v = |u| |v| cos(theta)

Answer 2

So, like this.
u dot v = (5 x -3) + (20 x 6) ?

Answer 3

\[u.v=\left| u \right|\left| v \right|\cos \]
\[\left( 5i+20j \right).\left( -3i+6j \right)=\sqrt{5^{2}+20^{2}}\sqrt{\left( -3 \right)^{2}+6^{2}}\cos \theta \]
\[\left( 5 \right)\left( -3 \right)+\left( 20 \right)\left( 6 \right)=\sqrt{425}\sqrt{45} \cos \theta \]
\[\frac{ 105 }{ 5\sqrt{17}3\sqrt{5} }=\cos \theta \]
\[\cos \theta=\frac{ 7 }{ \sqrt{85} },\theta =\cos^{-1} \frac{ 7 }{ \sqrt{85} }\]

Answer 4

theta is missing in the beginning.

Answer 5

Thank you so much! I really appreciate your help. Vectors aren't my strongest subject in PreCal. Thanks again!

Answer 6

yw