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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.
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 the sum of two vectors be a scalar?
No.
Is it scalar or vector when a car stops at a stop sign?
It is neither a scalar or a vector? Scalar and vectors are used to describe quantities, for example scalars include distance and mass, while vectors include weight and velocity. We do not say that a situation is a scalar or a vector.
Can sum of two vectors be numeric?
No, the sum of two vectors cannot be a scalar.
How do you represent the 1000000 in vectors?
1000000 is a number and therefore it is a scalar. A scalar cannot be represented as a vector.
Why scalar product are commutative?
i think that scalar product are commutative because the vectors are in the same direction
Is it possible the add a vector and scalar?
no!!!only scalars and scalars and only vectors and vectors can be added.
Do vectors have a direction?
Yes, vectors must have the direction. Without direction, it is simply a scalar quantity.
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.
What is the product of two vector quantities?
It depends on the type of product used. A dot or scalar product of two vectors will result in a scalar. A cross or vector product of two vectors will result in a vector.
Does the scalar product of two vectors depend on the choice of coordinate system?
No.
