Originally Posted by **avito009** Let me clarify why I have doubt that a scalar cant be negative. One of the definitions of scalar would be this:
Lets say we have an acceleration of -5 m/s (Deceleration actually). Now whats its scalar? Its |5| which is 5. Notice that the negative sign is dropped. So this made me think that a scalar is always positive in Euclidean space. |

You are making a number of threads which can make it hard to collate everything.

A vector cannot be positive or negative... It is not a number. If there is a negative involved then it must be from the scalar.

Let's get out of 1-D for a moment. Consider the vector $\displaystyle \textbf{v} = 5 \hat{i} - 2 \hat{j} + 3 \hat{k}$. Is this positive or negative? There is nothing to determine it one way or another so we can't say that it is either.

By the way, you

*really* need to work on your units. m/s is the unit for a speed, m/s^2 is the unit of an acceleration.

-Dan

PS I'm sorry, I keep finding things to add. You say that your vector -5 has a scalar |-5| = 5. This is the length or size or more properly "norm" of the vector. It is a scalar but a vector does not have "a scalar" in this sense. There can be many properties of a vector that are real numbers.