(adsbygoogle = window.adsbygoogle || []).push({}); Using the definitions in equations 1.1 and 1.4, and appropriate diagrams, show that the dot product and cross product are distributive;

(a) when the three vectors are coplanar;

(b) in the general case.

Eq. 1.1)AdotB= ABcosθ

Eq. 1.4)AcrossB= ABsinθN

This is exactly how my book puts the formulas.

I know how the definition of the dot product is derived, and that it's distributive over vector addition, but I don't understand why they're asking why thethreevectors are coplanar. I don't see where the third vector comes into play. I haven't even tried solving this on the cross product side because I know if I don't conceptually grasp the dot product part of it the cross product will only frustrate me.

Here's my attempt at this proof:

Part A: Stared at it for a while trying to figure it out and eventually gave up.

Part B: Broke out the comfort food. Cried a little.

1.2 Is the cross product associative?

(Vector A cross Vector B) cross vector C (equals?) Vector A cross (Vector B cross Vector C)

I know the cross product isn't associate because the order of the cross product determines the direction of the resultant vector, but I feel like there's more to it.

Thank you all so much for your help!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Proving distributivity of Dot/Cross product

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