# Cross product

No, that cross product is not zero. The dot product of u with it is zero.
If you have a triple product a.(b x c) and a is parallel to either b or c then the triple product is zero. The reason is clear: b x c is perpendicular to b and c; if a is parallel to b then a is perpendicular to b x c.
since the rE x W and rb xTB are not perpendicular to u , so it,s not = 0 ?
how do u knw that a is parallel to b then a is perpendicular to b x c ??

haruspex
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how do u knw that a is parallel to b then a is perpendicular to b x c ??
The cross product of two vectors (if nonzero) is always perpendicular to the two vectors.
If a is parallel to b then it must be perpendicular to b x c.

The cross product of two vectors (if nonzero) is always perpendicular to the two vectors.
If a is parallel to b then it must be perpendicular to b x c.
how do u knw that the rE x W and rb xTB are not perpendicular to u ????

haruspex
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Gold Member
2020 Award
how do u knw that the rE x W and rb xTB are not perpendicular to u ????
Why would that matter? Nothing in the algebra assumes those are not zero.

Why would that matter? Nothing in the algebra assumes those are not zero.
because when rE x W and rb xTB are not perpendicular to u , then i cant say that u . (rE x W) and u .(rb xTB ) = 0

haruspex