Let's say I have 2 unit vector of X and Y. I have to find another vector of Z. So if I were to cross X and Y to get Z, will Z also be a unit vector?
If you cross 2 unit vector, do you also get another unit vector at the other axis?
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vectors
cross-product
1 Answers
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We know that the magnitude of the cross product of $\vec x $ and $\vec y $ is given by: $$|\vec x \times \vec y| = |\vec x||\vec y| \sin \theta $$ where $\theta $ is the angle between the two vectors.
Now consider what will happen if $\vec x = \vec y $. Even if $\vec x \neq \vec y $, we do have, $|\vec x|=|\vec y| = 1$. Thus, $$ |\vec x \times \vec y| = \sin \theta $$
Hope you can take it from here.
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0I believe he's asking about when x and y are unit vectors, not the case that x = y. Besides the last statement, though, it does answer his question :) – 2017-02-08
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1@AliasUser Even if $\vec x \neq \vec y $, we do have $|\vec x| = |\vec y|=1$. Thus $|\vec x \times \vec y| = \sin \theta $. Then, $\cdots $? – 2017-02-08
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0Good point -- thank you! – 2017-02-08