Posted by Heather on .
Let u=j+k and v=i+jsqrt2.
a) Calculate the length of the projection of v in the u direction.
b) Calculate the cosine of the angle between u and v.
Your help is very much appreciated!

Calculus 3 
Reiny,
u = (1,1) , v = (1,√2)
The projection of v on u
= v.u/u
= (1 + √2)/√(1^1+1^1) = (1+√2)/√2
or (√2+2)/2
b)
u.v = uvcosØ
1+√2 = √2 √3 cosØ
cosØ = (1+√2)/√6 or (√6 + 2√3)/6 
Calculus 3 
Heather,
i'm confused on how you got u=(1,1) and v=(1,sqrt2). Shouldn't they each have 3 coordinates?
u=<0,1,1> and v=<1,sqrt2,0> ???