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Wiliam Rowan Hamilton, in 1843 invented vectors and scalars as components of his Quaternions. A quaternion consists of a scalar 1 and three vectors I,J and K. Hamilton's Quaternions represent a four dimensional Division Algebra and includes the Real numbers, the Complex numbers.
Relativity and Quantum Theory are unified in Quaternions. Relativity properly defined involves four dimensional Quaternions and Quantum Theory properly defined is Quaternions including non-commutativity, non-commutativity, Vector=AB-BA.
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Why is scalar product two vectors a scalar?
Scalar product of two vectors is a scalar as it involves only the magnitude of the two vectors multiplied by the cosine of the angle between the vectors.
Can sum of two vectors be numeric?
No, the sum of two vectors cannot be a scalar.
Why scalar product are commutative?
i think that scalar product are commutative because the vectors are in the same direction
Why the product of two vectors is sometime scalar and sometime vector?
Because there are two different ways of computing the product of two vectors, one of which yields a scalar quantity while the other yields a vector quantity.This isn't a "sometimes" thing: the dot product of two vectors is always scalar, while the cross product of two vectors is always a vector.
How are scalar and vector different?
Vectors have direction. Scalars don't.
