# Question: guided proof prove that if u is orthogonal to...

###### Question details

**Guided Proof :**

Prove that if **u** is orthogonal to
**v** and **w**, then **u**
is orthogonal to *c***v** +
*d***w** for any scalars *c* and
*d*.

Getting Started: To prove that **u** is orthogonal
to *c***v** + *d***w**, you
need to show that the dot product of **u** and
*c***v** + *d***w** is
0.

(i) Rewrite the dot product of **u** and
*c***v** + *d***w** as a
linear combination of (**u** _ **v**) and
(**u** _ **w**) using Properties 2 and 3
of Theorem 5.3.

(ii) Use the fact that **u** is orthogonal to
**v** and **w,** and the result of part
(i), to lead to the conclusion that **u** is
orthogonal to *c***v** +
*d***w**.