vector
scalar
A velocity potential is a scalar function whose gradient is equal to the velocity of the fluid at that point. If a fluid is incompressible and has zero viscosity (an ideal fluid) its velocity as a function of position can always be described by a velocity potential. For a real fluid this is not generally possible.
A scalar is a magnitude that doesn't specify a direction. A vector is a magnitude where the direction is important and is specified.
The product of a vector and a scalar is a new vector whose magnitude is the product of the magnitude of the original vector and the scalar, and whose direction remains the same as the original vector if the scalar is positive or in the opposite direction if the scalar is negative.
The equation that connects the scalar potential (V) and the vector potential (A) is given by: E = -∇V - ∂A/∂t, where E is the electric field, ∇ is the gradient operator, and ∂t represents the partial derivative with respect to time.
vector
Temperature gradient is a vector quantity. It represents the rate of change in temperature with respect to position and has both magnitude and direction.
Electric potential is a scalar.
Gravitational potential energy is a scalar quantity. It only depends on the height of an object above a reference point and does not have a direction associated with it.
Electrostatic potential is a scalar quantity. It represents the potential energy per unit charge at a given point in an electric field.
Electrical Potential Energy is a scalar or real number. Ep = zc e2 /4pi r.Total Energy is a Quaternion, the sum of the real or potential energy and the vector energy, Ev= mcV;E = Es + Ev = zc e2 /4pi r + mcV where Ev = mcV and V is the vector velocity.
Potential energy is a scalar quantity. Energy is the sum of a scalar part and a vector part. Energy W is the product of velocity V and momentum P; W = [c+V]P =[ -V.P + cP]. The Potential energy is the scalar energy -V.P=-vmv = -mv^2.Physicists consider energy a scalar quantity, but that is incorrect, energy is a Quaternion quantity, a scalar and a vector . The vector energy is the "Dark Energy" is hidden in plain sight, cP.
Electric potential is a scalar quantity since work done and charge are scalars
A scalar times a vector is a vector.
vector
An electromagnetic four-potential is a relativistic vector function from which the electromagnetic field can be derived. It combines both an electric scalar potential and a magnetic vector potential into a single four-vector.