No.
Because vectors have direction as well as magnitude, you must take the direction into account when you add them.
Example:
Vector A parallel to [0,0; 0,4]
Vector B parallel to [0,0; 3,0]
These vectors are at right angles to each other Vector A has a magnitude of 4, Vector B an magnitude of 3.
A + B = has a magnitude of 5, parallel to [0,0;3,4]
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Answer: A vector is always the product of 2 scalars
Vectors have direction. Scalars don't.
Because scalars do not take in the direction but just the magnitude while vectors can. You can add vectors ONLY if they are in the same direction.
Heat is energy. It and temperature are both scalars.
It is not possible the addition of scalars as well as vectors because vector quantities are magnitude as well as direction and scalar quantities are the only magnitude; they have no directions at all. Addition is possible between scalar to scalar and vector to vector. Under some circumstances, you may be able to treat scalar quantities as being along some previously undefined dimension of a vector quantity, and add them that way. For example, you can treat time as a vector along the t-axis and add it to an xyz position vector in 3-space to come up with a four-dimensional spacetime vector.