What is the angle between the vectors u 1 4 3 and v 2 5 1

What is the angle between the vectors u = (-1, 4, 3) and v = (2, 5, 1) 26.5 degree 37.3 degree 39.9 degree 41.2 degree 43.1 degree

Solution

u=<-1,4,3>

I u I= sqrt(-1²+4²+3²)=sqrt26

v=<2,5,1>

I v I=sqrt(2²+5²+1)=sqrt30

u.v= -1*2 + 4*5+3*1= 21

u.v=I u I I v I cos theta

21= sqrt(780) cos theta

cos theta=21/sqrt780

theta= 41.2 degree

Correct option is d