The dot-product of two vectors is the product of their magnitudes multiplied by

the cosine of the angle between them. The dot-product is a scalar quantity.

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

No. The dot product is also called the scalar product and therein lies the clue.

We use the dot product cos and in vector we use the vector product sin because of the trigonometric triangle.