In my class I have learned that the cross-product of two vectors are perpendicular to those two vectors. Teacher says it has something to do with torque. If it is, then 'if we have to open a door it should be easy to open it by exerting force on top of the hinge', but we know it is not. Is there any scientific reasoning to this question, or is it a standard way of multiplying vectors?
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It is just a mathematical truth that follows directly from the definition of the cross product of two vectors. You do not have to know anything about torque, or physics, to understand this. Two (non-zero) vectors $\vec{a}, \vec{b}$ are perpendicular if and only if their dot product vanishes, i.e. $\vec{a} \cdot \vec{b} = 0$. Can you show that $(\vec{a} \times \vec{b}) \cdot \vec{a} = (\vec{a} \times \vec{b}) \cdot \vec{b} = 0$? – jkb1603 Oct 22 '20 at 14:37
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Possible duplicates: https://physics.stackexchange.com/q/587917/2451 and links therein. – Qmechanic Oct 22 '20 at 15:06