Question

How do you find the angel between u=5i-4j, v=2i+j?

Answer 1

Use the dot product definition
`u.v=∥u∥∥v∥cos(u,v)`
`cos(u,v)=(u.v)/(∥u∥∥v∥)`
`u.v=5*2-4*1=6`
`∥u∥=sqrt(5^2+4^2)=sqrt41`
`∥v∥=sqrt(2^2+1^2)=sqrt5`
`cos(u,v)=6/(sqrt41.sqrt5)=0.6266`
`(u,v)=0.894 rd`