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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.
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
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.
Is it possible the add a vector and scalar?
no!!!only scalars and scalars and only vectors and vectors can be added.
Can a scalar product be a negative quantity?
Yes, a scalar product can be negative if the angle between the two vectors is obtuse (greater than 90 degrees). The scalar product is the dot product of two vectors and is equal to the product of their magnitudes and the cosine of the angle between them. A negative scalar product indicates that the vectors are pointing in opposite directions.
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.
Multiplying or dividing vectors by scalars results in?
Vectors. A scalar times a vectro is a vector. A vector times a vector is a scalr if the vectros are parallel v1.v2 = scalar. A vector times a vector is a vector if the vectors are perpendicular. Other wise a vectro times a vector is both a scalr and a vector, v1v2 = -v1.v2 + v1xv2 = -v1v2cos(x) + vqv2sin(x). If cos(x) =0 then perpendicular if sin(x)=0 then parallel. In general the product of two vectors is a quaternion the sum of a scalar and a vector. The Universe is composed of quaternions. Science and Physics has failed to appreciate that the numbes of the universe are quaternions, the sum of a scaltr and a vector. Hamilton invented quaternions in 1843.
How are scalar and vector different?
Vectors have direction. Scalars don't.
What is the difference between scalar and vector products of two vectors?
The scalar product (dot product) of two vectors results in a scalar quantity, representing the magnitude of the projection of one vector onto the other. The vector product (cross product) of two vectors results in a vector quantity that is perpendicular to the plane formed by the two input vectors, with a magnitude equal to the area of the parallelogram they span.
Can a scalar product by a negative quantity?
Yes, a scalar product can be negative if the angle between the two vectors is greater than 90 degrees. In this case, the dot product of the two vectors will be negative.
