Why is the magnitude of a vector always positive

Vectors have magnitude and direction. The magnitude is always a positive number. If all the components of a vector are zero, the magnitude of the vector will always be zero. Magnitude and Direction. It is a vector because it has a magnitude and a direction it can be positive or negative.

A positive scalar multiplied by a vector, will only change the vector's magnitude, not the direction. A vector at least, the vectors commonly used in physics has a length and a direction, and the way vectors are defined, this length but not the vector itself is always positive, or zero. It is the positive square root of its length. The magnitude of a vector is always treated as non negative and the minus sign indicates the reversal of that vector through an angle of degree.

It is customary to use only positive or zero values. Of course, a vector with a negative value would be equivalent to a positive vector in the opposite direction. It is a vector whose magnitude is 1.

When a scalar quantity if it has positive magnitude is multiplies by a vector quantity the product is another vector quantity with the magnitude as the product of two vectors and the direction and dimensions same as the multiplied vector quantity e. Magnitudes are positive. When we say that a vector has magnitude and direction, we assume the magnitude is positive and the direction is the actual direction of the vector quantity in question.

This is a convention. That said, the answer to the question is that the magnitude of the vector is taken as positive and the direction is a vector of unit length pointing in the same direction as the given vector.

If someone wants to do it differently, that is fine. They would not be wrong. A vector is described by magnitude and direction a scalar has only magnitude. That depends on what the vector, itself, represents.

For example, if the vector represents velocity, then the magnitude of the vector represents speed. If the vector represents displacement, then the magnitude of the vector represents distance. A null vector has no magnitude, a negative vector does have a magnitude but it is in the direction opposite to that of the reference vector. Vector b would be along the z axis, it could have any magnitude.

The magnitude of a vector is a scalar. A vector has both magnitude and direction. The magnitude is always positive, by convention, but this is not cast in stone. So you can have in your case a positive magnitude with a direction One could also say a negative magnitude at So there are many choices, and you seem to have a good handle on this. Log in. Study now. See Answer. Best Answer. Magnitude is the absolute value which is always positive.

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It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search. If components of a vector can be positive OR negative OR zero, why must the magnitude of a vector always be non-negative? A vector is a quantity described by a magnitude and a direction.

A -ve sign in front of a vector indicates the same magnitude but in the opposite direction. The - sign is part of the direction rather than the magnitude.

They are the projections of a vector onto the x and y axes or other axes. I apologise that this answer may not be mathematically rigorous.

The whole issue is confusing, as your question shows. I am trying to distinguish between the different terms being used. Sign up to join this community. The best answers are voted up and rise to the top.

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