Orthogonal Vector Set Question

Suppose v1,v2,v3 form an orthogonal set of vectors in R^5. Let w be a vector in Span{v1,v2,v3} such that

v1⋅v1=10
w⋅v1=4

v2⋅v2=29
w⋅v2=22

v3⋅v3=14
w⋅v3=8

Then w = _v1 + _v2 + _v3?

How can you figure this question out? I'm stumped.

Thank you!

have w = k1*v1 + k2*v2 + k3*v3. Use this in the second equation:

4 = = = = k1* = k1*10 => k1 = 0.4.

The third equality follows because v1,v2,v3 are orthogonal: == = 0.

Similarly you see that k2 = 22/29 = 0.75862, and k3 = 8/14 = 0.571428