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Chapter 9: Q. 43 (page 613)

Prove the polarization identity,

u+v2-u-v2=4u路v

Short Answer

Expert verified

u+v2-u-v2=4u路v

Step by step solution

01

Step 1. Given information

We have to prove the polarization identity

u+v2-u-v2=4u路v

02

Step 2. Proof

We can write u+v2as u+v路u+v

and u-v2as u-v路u-v

Now,

role="math" localid="1646800338985" u+v2-u-v2=u+v路u+v-u-v路u-v=u路u+u路v+v路u+v路v-u路u-u路v-v路u+v路v=u路u+u路v+v路u+v路v-u路u+u路v+v路u-v路v=2u路v+2v路u

Using commutative property, u路v=v路u

So,

2u路v+2v路u=4u路v

Therefore,u+v2-u-v2=4u路v

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Most popular questions from this chapter

Identify and graph each polar equation. Verify your graph using a graphing utility.
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