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Vectors and scalars are components of complex numbers. Complex numbers are z= x + iy, with one vector iy. The difference between the scalar part x and the vector part iy is, the square of the real part x is positive x^2 and the square of the vector part iy is negative -y^2. This square rule is what distinguishes scalars from vectors. Complex and Real Numbers are a subset of Quaternion Numbers.
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Quaternion q=w + ix + jy + kz = qw + qv contains one scalar (qw=w) and
three vectors (qv=Ix +jy + kz), . The three vectors make for a different rule for multiplication.
When there is only one vector the rule for multiplication is called commutative and AB=BA. This rule is what is generally taught in mathematics and science. Howver when there is more than one vector like in real world mathematics and science AB does not equal BA. This is called Non-commutaive mathematics.
Non-commutaive mathematics is the mathematics of of Quantum Physics. Quaternions provide the Unification of Relativity and Quantum Theory. Quaternions provide the correct four dimensions of Relativity Theory and the Non-Commutativity of Quantum Theory.
The general rule for multiplication of quaternions
AB= (AwBw -Av.Bv) + (AwBv + AvBw + AvxBv)
If the vectos Av and Bv are parallel AvxBv is zero and multiplication is commutative. If there is only one vector i like in complex numbers then AvXBv is always parallel ixi=0.
If the vectors Av and Bv are not parallel then multiplication is non-commutitive. Guess what most of the time things are not parallel in math and physics.
Scalars and vectors are very different and make up the two parts of numbers in math and science. Quaternions are the only kinds of numbers that can provide unique ( associative (AB)C = A(BC) ) division, such that you can solve equations like Ax=B.
Quaternion multiplication is all around us. Riding a bycycle uses quaternion math just like a gyroscope. Rotations in space requires quaternion multiplication.
It is important to distinguish between scalars and vectors and time to learn quaternion mathematics and understand the real world..
What else can I help you with?
Do vectors have quantity?
Both scalars and vectors have quantity. The difference is a vector has quantity and direction, whereas scalars only have quantity.
What is the difference between vector addition and algebraic addition?
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
Is a scalar a component of a vector?
Answer: A vector is always the product of 2 scalars
Is it possible the add a vector and scalar?
no!!!only scalars and scalars and only vectors and vectors can be added.
What are difference between scalars and vectors?
What are difference between scalars and vectors
How are scalar and vector different?
Vectors have direction. Scalars don't.
Is heat a scalar or vector?
Heat is energy. It and temperature are both scalars.
What word indicates the difference between vector and scalar measurements?
Direction. A scalar has only magnitude, while a vector has both magnitude and direction.
Why is the difference between scalars and vectors important?
Without the difference between scalars and vectors the Universe doesn't work !
One difference between vectors and scalars?
Vectors have a direction associated with them, scalars do not.
What is the difference between a scalar quantity and a vector?
Scalars are quantities that have magnitude only; they are independent of direction. Vectors have both magnitude and direction. vectors need bold letters to show them.
What are Scalar and vector values?
scalars are those quantities which have magnitude as well as unit.and vector are those quantities which has magnitude,unit as well as direction.
