How would I find the angle between vectors #u# & #v# if #u##=##i#+#4j# & #v##=##-i#+#2j#?

1 Answer
Oct 8, 2015

I found #40.6^@#

Explanation:

I wold try using the Scalar (dot) Product between them:
We have: either (using the components):
#vecu*vecv=u_xv_x+u_yv_y=(1*-1)+(4*2)=-1+8=7#
or:
#vecu*vecv=|vecu|*|vecv|*cos(theta)#

where #theta# is the angle between the two vectors:

#|vecu|=sqrt(1^2+4^2)=sqrt(17)#
#|vecv|=sqrt((-1)^2+2^2)=sqrt(5)#

Now we can use the two versions together:
#u_xv_x+u_yv_y=|vecu|*|vecv|*cos(theta)#

#7=sqrt(17)sqrt(5)cos(theta)#
#theta=cos^-1(7/(sqrt(17)sqrt(5)))=40.6^@#