Question

Prove that vectorA . (vectoraAXvectorB) = 0.
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Answer 1

Answer:

vector A X vector B can will any value but when its dot product is done with vector A the answer becomes 0 because dot product of two vectors perpendicular to each other is always 0.

vector A  and vector B are both perpendicular to  the plane so are perpendicular to each other and so is their cross product.

hope it helps

Answer 2

Answer:

AxB is perpendicular to both A and B so the dot product of A and AxB are perpendicular and dot product of perpendicular vector is equal to 0