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The sum of two null vectors is a null vector. And since a direction is not relevant for a null vector, the resultant has no direction either.

Q: How do you add two null vectors by following vector laws of addition?

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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.

Following the laws of mathematics, in this case the division will be done first, then the multiplication and then the addition. 8 ÷ 2 + 3 x 5 = 19

The Law of 4 Laws of addition and multiplication Commutative laws of addition and multiplication. Associative laws of addition and multiplication. Distributive law of multiplication over addition. Commutative law of addition: m + n = n + m . A sum isn't changed at rearrangement of its addends. Commutative law of multiplication: m · n = n · m . A product isn't changed at rearrangement of its factors. Associative law of addition: ( m + n ) + k = m + ( n + k ) = m + n + k . A sum doesn't depend on grouping of its addends. Associative law of multiplication: ( m · n ) · k = m · ( n · k ) = m · n · k . A product doesn't depend on grouping of its factors. Distributive law of multiplication over addition: ( m + n ) · k = m · k + n · k . This law expands the rules of operations with brackets (see the previous section).

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No, changing order of vectors in subtraction give different resultant so commutative and associative laws do not apply to vector subtraction.

A variety of mathematical operations can be performed with and upon vectors. One such operation is the addition of vectors. Two vectors can be added together to determine the result (or resultant). This process of adding two or more vectors has already been discussed in an earlier unit. Recall in our discussion of Newton's laws of motion, that the net force experienced by an object was determined by computing the vector sum of all the individual forces acting upon that object. That is the net force was the result (or resultant) of adding up all the force vectors. During that unit, the rules for summing vectors (such as force vectors) were kept relatively simple. Observe the following summations of two force vectors:

No, the order of addition of individual vectors does not affect the final resultant vector as vector addition is commutative. This means that the final result will be the same regardless of the order in which the vectors are added.

No. A vector is actually a first order tensor as opposed to all tensors being vectors (vector quantities could be considered a subset of the set of all tensor quantities) because if you were to take a vector in three spatial dimensions A it can be defined by the equation A=A1e1+A2e2+A3e3 and also follows the tensor transformation laws given by A'i=αi'kAk for instance. Tensors however are actually more generalised objects which include vectors, scalars (zeroth order tensors) and more complicated systems.

It has magnitude 0 and a direction and obeys vector laws, so is a vector

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.

Yes. Vectors follow the same laws as simple scalars. For example A + B = C ; (A1 + A2) + (B1 +B2) = (A1 + B1) + (A2 + B2) = C1 + C2 where C1 = A1 + B1 and C2 = A2 + B2.

Scalar quantity is the usual one. It is already there unavoidable. But vector is the new one. Why do we need it? Suppose say two persons by name John and Johann push a box with forces 4N and 3N, what could be the effective force on the box? One may say 7 N by adding them. One may say just 1N because of getting the difference. Another may say 5N. How? Why do they give different answers? It is because the directions in which the forces acting are considered in different ways. If both in the same, addition is ok. If in opposite then difference is right one. If they are at right angles then pythagros technique. So direction is the most essential data to get the right answer. Hence magnitude with direction is known to be vector quantity.

1. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied. 2. The relationship between an object's mass (m), it's acceleration (a), and the applied force (F) is F=ma. Acceleration and force are vectors; in this law the direction of the force vector is the same as the direction of the acceleration vector. 3. For every action there is an equal and opposite reaction.

You need to say what the following laws are.

After leaving the gunbarrel, the only force preventing straight line motion is gravity, the result is (apart from firing straight up) a flight path in the form of a parobolic curve. Using the launch angle and velocity, break into horiontal and vertical velocity vectors. Horizontal velocity vector is contant horizontal velocity. Vertical velocity vector will obey newtons laws up and down Using time intervals, you can plot the curve.

No, it is a scalar. Energy is the capacity to do work. Answer2: Yes. Energy is a scalar and a vector. Energy is a Quaternion quantity consisting of a scalar and three vectors, forming a 4D quantity.Early scientists started with scalar quantities. With Faraday's field theory (directed lines), vectors came into physics. However, the early definition of energy as scalar persisted to this day. Vector energy is all around us, but we are blinded by dogma. F.D is called energy, but FxD is vector energy but is called Torque. I think we are about to lift the blindness. "Dark Energy" in Astronomy is vector energy. The Dark Energy is cmV = cP. Here is vector energy, Momentum energy. Momentum is a vector and Momentum energy cP is also a vector. A scalar c times a vector is a vector ! If there is vector momentum, there must be vector energy! The correct Equation off Gravitation Energy is E = -mGM/r + mcV = -mu/r + cP. Newton did not include the vector energy cP=cmV. This was equivalent to saying the mass m, had velocity zero , E= -mu/r + mc0. Such is NOT the case. This is like saying the earth is orbiting the sun with velocity 0, when it is moving at 30km/s. it is the vector energy cmV that provides the centrifugal force to keep the earth from falling into the sun. It is the vector energy that is the "dark Energy" that is the anti-gravity (centrifugal) force. Vector Energy removes teh mystery of "Dark Energy". Newton's Three laws are derived from this vector energy, that Newton incorporated. Force F = XE = [d/dr, DEL] m[-u/r , cV] F = m[v2/r - cDEL.V, cdV/dr +u/r3 R + cDELxV] At Equilibrium 0 = F and DELxV=0 meaning R and V are parallel and. It is essential that DELxV =0 for the vectors to sum to zero. The result is 0 = m[v2/r - cv/r, cdV/dr + u/r3 R ] Equilibrium Condition exists when v/c=1 or v=c. Newton's Equal and Parallel phrase comes form 0 = m(dV/dt + u/r3 R) comes from 0 = cdV/dr - DEL u/r Newto added the term 'mdV/dt' a vector, before vectors, This term is the vector energy P=cmV and dcP/dr = cmdV/cdt = mdV/dt, voila! It is time to recognize that we live in a 4D Universe and Energy is a 4D Quantity.