it is physically the projection or shadow of a line on a plane...
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here are the possible answers: A) A tridimensional vector B) A 4D vector C) A 5D vector D) An scalar number E) It is undefined
If by "triple dot product" you mean u·v·w, then no, because that would imply the existence of a dot product between a vector and a scalar.
cross: torque dot: work
We use the dot product cos and in vector we use the vector product sin because of the trigonometric triangle.
It depends on what the dot product is meant to be equal to.