Hello,

I don't understand why vw in what you wrote ??

If u is orthogonal to v, it means that u.v=0, where . denotes the dot product.

We have :

u.v=0

u.w=0

What is the dot product of u with v+w ?

u.(v+w)=u.v+u.w, by a property (*) of the dot product.

And this equals 0 by the hypothesis. Hence u is orthogonal to v+w.

Same reasoning for the other one (you'll have to use properties (*) and (**))

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