Calculate | $vec u$ + $vec v$ | help?

Question

Given that | $vec u$ | = 3 and | $vec v$ | = 4

ALSO
calculate the angle between $vec u$ and
$vec u$ + $vec v$

1665 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-09T06:55:16

See below

First Part

$abs bb u = 3, abs bb v = 4, phi = (2pi)/3$

$abs(bb u + bb v)^2 = (bb u + bb v )*(bb u + bb v )$

$= u^2 + v^2 + 2 bb u * bb v$

$= 3^2 + 4^2 + 2 * 3 * 4 * cos(120)$

$=13$

$implies abs(bb u + bb v) = sqrt13$

Second Part

$bb u * (bb u + bbv) =abs bb u * abs (bb u + bbv) cos theta$

$cos theta = (bb u * (bb u + bbv))/ (abs bb u * abs (bb u + bbv) )$

$= (u^2 +abs bb u abs bb v cos phi)/ (abs bb u * abs (bb u + bbv) )$

$= (3^2 +3 * 4 * cos (120))/ (3 * sqrt(13) )$

$= 1/sqrt(13)$

$theta = cos^(-1) (1/sqrt(13)) = 73.9^o$