Posted by **Heather** on Wednesday, January 16, 2013 at 11:18pm.

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**, Thursday, January 17, 2013 at 12:07am
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 = |u||v|cosŲ

1+√2 = √2 √3 cosŲ

cosŲ = (1+√2)/√6 or (√6 + 2√3)/6

- Calculus 3 -
**Heather**, Thursday, January 17, 2013 at 11:52am
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> ???

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