- #1
Saladsamurai
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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 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?
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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