vectors u = & v= , find angle between u & v and projection where proj(v)u=(u*v/|v|^2)v thank you for help!

We are asked to find the angle between vectors u and v and
the projection where proj(v)u = (u*v/|v| ^ 2)v.

u=
<5,8> and v = <20,5>.

We will
first find the angle between vectors u and v.

The formula
is cos(theta) = (u *v)/(|u| *|v|)

=> cos (theta)
=

(5*20) + (8 * 5)/ [(sqrt 5^2 + 8 ^2) * (sqrt 20 ^ 2 + 5 ^
2)]

=> cos (theta)
=

(100 + 40)/(sqrt 25 +64) *(sqrt 400 +
25)

=> cos (theta) = (140) /(sqrt 89) *(sqrt
425)

=> cos (theta) = (140) / (sqrt
37825)

=> cos (theta) =
(140)/(194.4865)

=>  The angle between
the two vectors is approximately 43.96
degrees.

To find the projection we use the
following formula which we  were given:

=>
projection  (v)u =  (u * v/ |v| ^2) v

=> projection
(v)u =

{[(5 * 20) + (8 * 5)/[sqrt  (20 ^2 + 5 ^2)] }* (20,
5)

=> projection (v)u = [(140)/(sqrt 425) ] *
(20,5)

=> projection(v)u  = 6.79 * ( 20,
5)

=> projection(v)u = ( 135.8, 33.95
)

The angle between the two
vectors is approximately 43.96
degrees.

The projection(v)u =
( 135.8, 33.95 ).