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PLEASE Skip to post #14 after reading problem statement; I am trying to solve this without using components

Griffith's E&M problem 1.1. I feel good about my life.

Using the definition [itex]\vec{A}\cdot\vec{B} =AB\cos\theta[/itex] show that the dot product is distributive when

(a) the 3 vectors are coplanar

(b)the general case

Okay then for part (a) I have started like this:

Let

then

[tex]\vec{A}\cdot(\vec{B}+\vec{C})=|\vec{A}||\vec{B+C}|\cos\gamma[/tex]

where gamma is the angle between

...now I am a little confused, i want to write that this implies

[tex]\vec{A}\cdot(\vec{B}+\vec{C})=(AB+AC)\cos\gamma[/tex]

but I am not sure if that is correct. And if it is, where to go from here?

## Homework Statement

Griffith's E&M problem 1.1. I feel good about my life.

Using the definition [itex]\vec{A}\cdot\vec{B} =AB\cos\theta[/itex] show that the dot product is distributive when

(a) the 3 vectors are coplanar

(b)the general case

Okay then for part (a) I have started like this:

Let

**A****B**&**C**be 3 coplanar vectors. Let [itex]\theta[/itex] be the angle between**A**&**B**; let [itex]\phi[/itex] be between**B**&**C**and let [itex]\alpha[/itex] be between**A**&**C**then

[tex]\vec{A}\cdot(\vec{B}+\vec{C})=|\vec{A}||\vec{B+C}|\cos\gamma[/tex]

where gamma is the angle between

**A**and (**B+C**)...now I am a little confused, i want to write that this implies

[tex]\vec{A}\cdot(\vec{B}+\vec{C})=(AB+AC)\cos\gamma[/tex]

but I am not sure if that is correct. And if it is, where to go from here?

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