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William Rowan Hamilton invented the terms Scalars and Vectors with his Quaternions. Quaternions are the sum of a scalar and three vectors. Q=s + ix +jy + kz, = s +v where s is the scalar and ix,jy and kz are the vectors. The rule for vectors is i^2=j^2=k^2= ijk = -1.
Scalar and vector quantities are the two kinds of numbers. Scalar quantities are real number quantities having a positive square. s^2>0. Scalars are commutative s1s2=s2s1.
Vector quantities v, are directional numbers and have a negative square, V^2= -1.
Typical vector denotations are i ,j and k.
Vectors are non-commutative ij=-ji
There are false vectors used in physics today ala Gibbs Heaviside "vectors" where v^2=+1. These vectors are non-associative i(jk) does not equal (ij)k when v^2=+1.
Associativity is true when v^2= -1.
Quaternions the sum of a scalar and three vectors constitutes a four dimensional division space. This is only associative division space. Quaternions contains two associative division sub spaces, the Complex space (Reals + Imaginaries)) and the Real space (Reals).
There is another division space, Octonions consisting of reals and vectors but it is not associative.
What else can I help you with?
Is current a scalar or vector quantity?
It depends upon the condition.But basically, to be a vector, the physical quantities needs to follow vector algebra.but current dos not follow it so it is scalar quantity.
What is the difference between vector and scalar quantities?
Vector quantity is a quantity characterized by magnitude and direction.Whereas,Scalar quantity is a quantity that does not depend on direction.
Name scalar fields and vector fields?
name as many scalar fields and vector fields as u can?
Is a force of friction a vector or scaler quantity?
Either, or both. Motion can be described in either vector or scalar terms. Speed is a scalar quantity, having only a magnitude. Velocity is a vector quantity, having both magnitude and direction. Acceleration is a vector quantity.
Are the magnetic field vector- or scalar fields?
Both, E=Es + Ev = cB therefore, B= Es/c + Ev/c = Bs + Bv. The electric and magnetic fields are quaternion fields consisting of a scalar field and a vector field. Contemporary Physics has not realized this yet. Correct Relativity Theory is a manifestation of quaternion fields, consisting of a scalar field and three vector fields. This shows up in the Energy Momentum four vector, E= Es +cmV. Actually the Lorentz Force is both scalar and vector: F=qvB = - qv.B + qvxB it makes no sense consider only qvxB and to ignore qv.B.
Can a scalar quantity be the product of 2 vector quantities?
No, a scalar quantity cannot be the product of two vector quantities. Scalar quantities have only magnitude, while vector quantities have both magnitude and direction. When two vectors are multiplied, the result is a vector, not a scalar.
Similarities between scalar and vector quantities?
Scalar quantities - quantities that only include magnitude Vector quantities - quantities with both magnitude and direction
What are the quantities that identifies scalar and vector quantities?
A vector is characterized by having not only a magnitude, but a direction. If a direction is not relevant, the quantity is called a scalar.
Diffrentiate between vector and scalar quantities?
Scalar quantities are defined as quantities that have only a mganitude. Vector quantities have magnitude and direction. Some example of this include Scalar Vector Mass Weight length Displacement Speed Velocity Energy Acceleration
How are scalar and vector quantities similar?
Scalar and vector quantities are both used in physics to describe properties of objects. They both have magnitude, which represents the size or amount of the quantity. However, the key difference is that vector quantities also have direction associated with them, while scalar quantities do not.
Vector and scalar quantities definition?
Vector quantities have both magnitude and direction, such as velocity and force. Scalar quantities have only magnitude and no specific direction, such as speed and temperature.
Is a vector quantity is always the same as a scalar quantity?
No, a vector quantity and a scalar quantity are different. A vector has both magnitude and direction, while a scalar has only magnitude. Velocity and force are examples of vector quantities, while speed and temperature are examples of scalar quantities.
Are force and acceleration scalar quantities?
No. Force and acceleration are vector quantities.
How are scalar and vector quantaties alike?
Scalar and vector quantities are both used to describe physical quantities in physics. The key similarity between them is that they both involve numerical values. However, vector quantities also have a direction associated with them, while scalar quantities do not.
What are scalar and vector forces?
There is no such thing as scalar and vector forces. However, there are scalar and vector QUANTITIES, and force is a vector quantity, as all forces have direction and magnitude. Scalar quantities, on the other hand, have only magnitude and no direction.
Is work and energy scalar or vector quantities explain?
Work and energy are scalar quantities because they have magnitude but no direction. They are described by a single numerical value rather than having both magnitude and direction like vector quantities.
What is the quantities that has magnitude?
scalar quantities have magnitude only while vector quantities have both magnitude and direction. e.g.s of scalar quantities- distance, mass, temperature, speed e.g.s of vector quantities-displacement, velocity, acceleration, weight, force
