# How does crossing two 3d vectors produce a third one that is perpendicular to both? [duplicate]

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Can someone help me understand the cross product a little better, for me it makes more sense for the new vector to be somewhere between the original vectors and closer to the bigger one but that would be just adding to one another right? how does crossing say for example vector $\vec A \times \vec B =\begin{bmatrix} 1 \\ 0 \\ 0 \\\end{bmatrix} \times \begin{bmatrix} 0 \\ 1 \\ 0 \\ \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\ 1 \\\end{bmatrix}= \vec C$?

## marked as duplicate by David K, user137731, user147263, Andrew D. Hwang, Najib IdrissiOct 16 '15 at 16:40

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• What definition of the cross product did you learn? Are you having difficulty seeing how the definition leads to a perpendicular vector, or do you think "cross product" should have been defined differently? – David K Oct 16 '15 at 12:59
• I don't understand how multiplying different dimensions which is the crossing part of the cross product if I understand correctly leads to another dimension? so I guess how or where does the perpendicular vector come from and why wouldn't it be in the same plane as the original vectors? – Raed Oct 16 '15 at 13:04
• I don't know what you mean by "multiplying different dimensions" -- sounds pretty sci-fi, though. 😉 Maybe you should check out my answer to this question. – user137731 Oct 16 '15 at 13:14
• @Raed Oh. You're the guy who asked this question yesterday. Seriously spend some time reading through my (way too long) answer to the question I linked to. It might help you with some of your questions about the dot and cross products. – user137731 Oct 16 '15 at 13:25