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How can vectors be added in either order?
Addition is commutative, A + B = B + A.
Does the order of addition of indivitual vectors affect the final resultant vector and why?
The order of addition of individual vectors does not affect the final result. The reason is that "addition is commutative", meaning C=A +B = B + A. The laws of multiplication fro vectors is non-commutative and AxB = - BxA. Multiplication of vectors is non-commutative. Vectors and Reals make up our natural numbers called Quaternions . Given a quaternion A=Ar + Av where Ar is the real part of A and Av is the vector part of A and B=Br +Bv, the product is: AB=(Ar + Av)(Br + Bv)= (ArBr - Av.Bv) + (ArBv + AvBr + AvxBv) If the vectors are perpendicular Av.Bv=0, (the dot '.' denotes the cosine product). If the vectors are parallel AvxBv=0, (the cross 'x' denotes the sine product). Unfortunately quaternions multiplication is not taught in schools. Quaternions simplify algebra, trigonometry and vectors. Quaternions are also the natural numbers of the Universe.
Does the order of addition of indivitual vectors affect the final resultant vector?
no it does not affect the outcome
Why does the addition of vectors in a different order still result in returning to the same final position?
Addition is a commutative; A+B = B +A.
When adding vectors what do you have to be certain in?
When adding vectors, you have to make sure that they are being added tip to tail in the correct order. Additionally, ensure that the vectors are in the same coordinate system, so that the components can be added properly. Finally, double-check that the units of the vectors are consistent to ensure correct results.
What is the property of addition states that numbers can be added in any order?
It is the commutative property of addition.
Does the order of adding vectors affects the magnitude and direction of the vectors?
No. The order of adding vectors does not affect the magnitude or direction. of the result.
How is the resultant displacement affected when 2 displacement vectors are added in a different order?
Assuming your talking about simple math of vectors, each vector is made up of components in different directions and magnitudes. Vector=V=ui+vj+wk Where i is the unit vector in the x direction, v is in the y direction, and k is in the z direction. u,v,w are the components each of these directions. If North is in the y direction and East is in the x direction, then a person traveling at 50 mi/h in the Northeast direction would have a Velocity in both i and j direction V=ui+vj Where 50mi/h=25*sqrt(25)i+25*sqrt(25)j V=sqrt{[25*sqrt(25)i]^2+[25*sqrt(25)j]^2}=50 All of this said, you simply add the components of the two vectors together, i's plus i's and j's plus j's.
How does the order that the vectors are combined affect the displacement?
The order in which vectors are combined affects the overall displacement because vector addition is not commutative. The resultant vector will be different depending on the direction and magnitude of each individual vector. To find the total displacement, you must consider both the direction and magnitude of each vector in relation to the others.
What could be the weakness or disadvantages of the tail-to-tip method of adding vectors?
One weakness of the tail-to-tip method is that it can be prone to errors in visualization, especially with complex vector arrangements. Additionally, it can be time-consuming for large numbers of vectors. Lastly, this method may not be as accurate when dealing with vectors in three-dimensional space.
The Property of addition states the the number can be added in any order and the sum will be the same?
associative property
What property of addition states that the numbers can be added in any order and the sum will be the same?
Associative Property
