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.
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
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.
In mathematics, the dot product is an algebraic operation that takes two equal-length sequences of numbers (usually vectors) and returns a single number obtained by multiplying corresponding entries and adding up those products. The name is derived from the interpunct "●" that is often used to designate this operation; the alternative name scalar product emphasizes the scalar result, rather than a vector result.The principal use of this product is the inner product in a Euclidean vector space: when two vectors are expressed in an Orthonormal basis, the dot product of their coordinate vectors gives their inner product. For this geometric interpretation, scalars must be taken to be Real. The dot product can be defined in a more general field, for instance the complex number field, but many properties would be different. In three dimensional space, the dot product contrasts with the cross product, which produces a vector as result.
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.
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Dot product is an algebraic operation when two equal-length sequences of numbers are returned as a single number.
They are the same.
A dot product is a scalar product so it is a single number with only one component. A cross product or vector product is a vector which has three components like the original vectors.