Question

Find |u+v| given that Theta (θ) is the angle between |u| and |v|
a.|u|=66, |v|=22, angle θ=44°

Answer 1

try finding
\[|u+v|^{2}=?\]
and then put a square on it

Answer 2

how does the angle come into play

Answer 3

it must involve some multiplication with sine or cosine

Answer 4

\[|u+v|^{2}=u^{2}+v^{2}+2uv(*)=|u|^{2}+|v|^{2}+|u||v|\cosθ=...\]
u*v=|u||v|cosθ (vector product)

Answer 5

and then plug the result u got at a square root to find the |u+v|

Answer 6

u got it?

Answer 7

im not getting the right answer

Answer 8

i dont understand the equation you typed out. i cant fathom it without numbers in it. its hard for me to understand things when steps are in a string

Answer 9

its easier to see equivalency when things are stacked when simplified or expanded

Answer 10

\[|u+v|^{2}=(u+v)^{2}=u^{2}+2uv+v^{2}=|u|^2+2uv(i)+|v|^{2} \]
for any vector: \[a^{2}=|a|^{2}\]
to get rid of (i) we use the vector product