- #1

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[itex]\vec{A}[/itex][itex]\times[/itex][itex]\vec{B}[/itex]=[itex]\vec{C}[/itex]

How to express [itex]\vec{A}[/itex] in term of [itex]\vec{B}[/itex] and [itex]\vec{C}[/itex] (or [itex]\vec{B}[/itex] in term of [itex]\vec{A}[/itex] and [itex]\vec{C}[/itex] ). I think the question I want to ask can also be rephrased as if one was told that a known vector when cross product with an unknown vector, yield a known vector, find the unknown vector.

Similarly,

Given the following dot product equation:

[itex]\vec{D}[/itex][itex]\bullet[/itex][itex]\vec{E}[/itex]=k

How to express [itex]\vec{D}[/itex] in term of [itex]\vec{E}[/itex] and k. Similarly also, the question I want to ask can be rephrased as if one was told that a known vector when dot product with an unknown vector, yield a known scalar, find the unknown vector.

My personal thought is, it can't be done. Never heard of a "division" in vector operation. But, maybe I am wrong.