I am doing some review on cross products, and I forgot how do a cross product similar to this: vQ xx B_1=vQ xx B_2 where Q,B_1,B_2 are vectors, xx is cross product, and v is a scalar.

zibazeleor

zibazeleor

Open question

2022-08-29

I am doing some review on cross products, and I forgot how do a cross product similar to this:
v Q × B 1 = v Q × B 2
where Q , B 1 , B 2 are vectors, × is cross product, and v is a scalar.
I would be trying to prove that B 1 and B 2 are equal to each other, other than saying that it is indeed true, but I don't know if an "inverse" cross product exists, and can't seem to figure out how to prove it exists, if it does. Any help would be awesome!

Answer & Explanation

Cora Bird

Cora Bird

Beginner2022-08-30Added 8 answers

I'll be using JMoravitz's interpretation of the problem.
Suppose for every nonzero scalar v and nonzero vector Q we have v Q × B 1 = v Q × B 2 . Then
v Q × B 1 v Q × B 2 = 0
v ( Q × B 1 Q × B 2 ) = 0
v ( Q × ( B 1 B 2 ) ) = 0
Since Q 0 , there's only one vector that crosses with any vector to yield 0 , namely 0 . Then B 1 B 2 = 0

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?