If a is a vector and c is a scalar, what is a+c?

Question

I just want to see how it works :)

maybe you could give me an example with numbers

Answer 1

You can't add a vector and a scalar, it's like trying to add age and weight.

Answer 2

You cannot add a vector and a scalar without making an assumption about the direction of the scalar, in which case it would become a vector also. You could add the scalar to the magnitude of the vector. I'm not sure if this makes much physical sense.

You asked for an example: The wind is blowing five meters/second (direction not given). That is a scalar. Relative to the air, an airplane is flying at 100 m/s (60 m/s north and 80 m/s west), which is a vector. Suppose I want to know the effect of the wind on the airplane.

I can simply add 5 m/s (air) to 100 m/s (plane), but that makes the implicit assumption that the plane has the wind at its back. If the wind is blowing east, that would subtract 5 m/s from the plane's east-west component, so, relative to the ground, it is flying 75 m/s west and 60 m/s north. By the Pythagorian theorem, its absolute speed is √(75² + 60²) or √(9225) m/s.

You can see why adding c to a doesn't work.

Answer 3

You cannot get a sensible answer by adding vector and scalar values. For example you cannot add a sum of money and a wind velocity and attach any useful meaning to the result.

Bramble

Answer 4

I don't think the addition operation is defined for vector against scalars. However, multiplication and division are.

Answer 5

Undefined. You cannot add a vector and a scalar, or in general add tensors of different ranks. (A vector is a tensor of rank 1, and a scalar is a tensor of rank 0.)

Answer 6

That's undefined. You cannot add a scalar to a
vector.

Answer 7

it does not work