Question 1183418
{{{abs(3u + 4v)^2

= (3u+4v)*(3u+4v)

= 9u*u + 24u*v + 16v*v

= 9abs(u)^2 + 24u*v + 16abs(v)^2

=9 + 24abs(u)*abs(v) + 16 = 25 +24abs(u)*abs(v)}}}, since u and v are unit vectors.

= {{{25 + 24abs(u)*abs(v)cos(theta)  = 25 + 24cos(pi/3) = 25 + 24*(1/2) = 37}}}.

Hence {{{abs(3u + 4v)^2 = 37}}}, which implies that {{{abs(3u+4v) = sqrt(37)}}}.