by this do you mean
s*V
where s is the scalar and V is the vector?
if V = ai + bj + ck then
s*V = (s*a)i + (s*b)j + (s*c)k
where i, j and k are the unit vectors and a,b and c are constants
Essentially you just multiply each part of the vector by the scalar
vector
scalar
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.
Since you can represent that with a single number, it isn't a vector - just a scalar.
It is not impossible to add a scalar to a vector. e.g. e^ix = cos(x) + isin(x) when x is 0 the answer is a scalar, when x=90 degrees the answer is a vector, when x is not a multiple of 90 degrees the answer is the sum of a scalar and a vector. So it is only impossible to add a scalar to a vector when x is a multiple of 90 degrees, all other angles add a scalar to a vector.
A scalar times a vector is a vector.
vector
Yes, you can add a scalar to a vector by adding the scalar value to each component of the vector.
Scalar
When multiplying a vector by a scalar, each component of the vector is multiplied by the scalar. This operation changes the magnitude of the vector but not its direction. Similarly, dividing a vector by a scalar involves dividing each component of the vector by the scalar.
A scalar quantity has an angle which is an even multiple of 90 degrees. A vector quantity has an angle which is an odd multiple of 90 degrees. A quaternion has any angle and includes the scalar and the vector; quaternion q = cos(angle) + unit-vector sin(angle)
An earthquake is neither a scalar nor a vector. It is an event.
vector
vector
Yes, you can multiply a vector by a scalar. The scalar will multiply each component of the vector by the same value, resulting in a new vector with each component scaled by that value.
It is scalar