Measurable quantities are vectors or scalars.
"Space" is not a measurable quantity.
"Volume" is. It's a scalar.
Vectors can be added to other vectors in the same vector space. Scalars can be added to other scalars if they have the same units. Scalars cannot be added to vectors, nor vice versa, directly.
No, force is a vector quantity because it has both magnitude and direction. Scalars have only magnitude and no specific direction.
It has both velocity and direction. A vector has direction and magnitude.
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.
The quantity "120 meters northeast" is a vector because it has both magnitude (120 meters) and direction (northeast). Scalars have magnitude only and no specific direction associated with them.
Answer: A vector is always the product of 2 scalars
no!!!only scalars and scalars and only vectors and vectors can be added.
I take the term 'number' in this context to mean the scalars by which vectors may be multiplied. These can be the elements of any field.
Vectors have direction. Scalars don't.
Both scalars and vectors have quantity. The difference is a vector has quantity and direction, whereas scalars only have quantity.
Heat is energy. It and temperature are both scalars.
Vectors can be added to other vectors in the same vector space. Scalars can be added to other scalars if they have the same units. Scalars cannot be added to vectors, nor vice versa, directly.
The zero vector occurs in any dimensional space and acts as the vector additive identity element. It in one dimensional space it can be <0>, and in two dimensional space it would be<0,0>, and in n- dimensional space it would be <0,0,0,0,0,....n of these> The number 0 is a scalar. It is the additive identity for scalars. The zero vector has length zero. Scalars don't really have length. ( they can represent length of course, such as the norm of a vector) We can look at the distance from the origin, but then aren't we thinking of them as vectors? So the zero vector, even <0>, tells us something about direction since it is a vector and the zero scalar does not. Now I think and example will help. Add the vectors <2,2> and <-2,-2> and you have the zero vector. That is because we are adding two vectors of the same magnitude that point in opposite direction. The zero vector and be considered to point in any direction. So in summary we have to state the obvious, the zero vector is a vector and the number zero is a scalar.
scalars are those quantities which have magnitude as well as unit.and vector are those quantities which has magnitude,unit as well as direction.
No they are scalars, though the rate of change could be a vector and the wind is definitely a vector (both direction and speed)
It depends on the angle between the vectors (AB). The product of two vectors Av and Bv is AvBv=-Av.Bv + AvxBv= |AvBv|(-cos(Ab) + vsin(AB)). If the angle is a odd multiple of 90 degrees the product is a vector. If he angle is an even multiple of 90 degrees, the product is a scalar. If he angle is not a multiple of 90 degrees, the product of a vector by another vector is a quaternion, the sum of a scalar and a vector. Most numbers in physics and science are quaternions, a combination of scalars and vectors.Quaternions forma mathematical Group, vectors don't. The product of quaternions is always a quaternion. The product of vectors may not be a vector, it may be a vector , a scalar or both. The product of scalars is also a Group. Vector by themselves do not form a Group. The Order of Numbers are Scalars form a Group called Real Numbers; scalars and a single vector form a group called complex numbers; scalars and three vectors form a group called Quaternions. These are the only Groups that provide an Associative Division Algebra.
There is no difference between vector addition and algebraic addition. Algebraic Addition applies to vectors and scalars: [a ,A ] + [b, B] = [a+b, A + B]. Algebraic addition handles the scalars a and b the same as the Vectors A and B