- #1

Jake 7174

- 80

- 3

## Homework Statement

Show that vector

**C**= (B

**A**+ A

**B**) / (A + B) is an angle bisector of

**A**and

**B.**Where

**vectors**are represented by

**bold**font, and magnitudes are regular font.

## Homework Equations

**A ⋅ C**= A C cos(θ) ⇒ cos(θ) = (

**A ⋅ C**) / (A C)

**B ⋅ C**= B C cos(θ) ⇒ cos(θ) = (

**B ⋅ C**) / (B C)

## The Attempt at a Solution

We know that if

**C**is a bisector of

**A**and

**B**, then ∠

**AC**=∠

**BC**= θ must be true.

I set the above equations equal to each other to get;

(

**A ⋅ C**) / (A C) = (

**B ⋅ C**) / (B C)

I notice the magnitude C cancels and then cross multiply the expression to get;

(

**A ⋅ C**)B = (

**B ⋅ C**)A

I bring the right side over and use identities of dot products to get;

**C**⋅ [B

**A**- A

**B**] = 0

This is where I am stuck I don't know how to take it any further. I would appreciate a push in the right direction.

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