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# The dot product and the cross product Watch

1. (Original post by B_9710)
Yes that's what the hat above the n means.
When you simply find the cross product of 2 non parallel vectors, say a and b your answer gives a vector that is perpendicular to both a and b, but this perpendicular vector does not necessarily have a magnitude of 1.
So if always has a magnitude of 1, why is it included in the cross product formula? Is it so it gives the cross product direction?
2. (Original post by Megan_101)
So if always has a magnitude of 1, why is it included in the cross product formula? Is it so it gives the cross product direction?
Because when you find the cross product of 2 vectors you get a normal vector and the magnitude of th vector is the product of the magnitude of the two vectors. If the was not in the formula then it would say that when you cross multiply two vectors that you get a scalar - which is not true - you get a vector.
3. maybe useful:
• to prove that two not null vectors are parallel, just prove that their cross product is zero.
• to prove that two not null vectors are perpendicular, just prove that their dot product is zero.
interesting:
Finding the absolute value of the dot product of a vector a with the cross product of two other vectors b and c, we find the volume of a parallelepiped with sides a, b, c.

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