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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.
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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.
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.
Will changing the order of your displacements in the vector diagram affect magnitude and direction?
No, changing the order of displacements in a vector diagram does not affect the magnitude or direction of the resultant displacement. The resultant displacement depends only on the initial and final positions, not the order in which the displacements are added.
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 two conditions must be met in order to convert angular displacement to linear displacement?
To convert angular displacement to linear displacement, you need to know the radius of the circle or rotation and the angle of rotation in radians. By multiplying the radius by the angle in radians, you can calculate the linear displacement.
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.
Does the order of addition of indivitual vectors affect the final resultant vector?
no it does not affect the outcome
What is the velocity vector equation?
You have to solve Newton's equation ΣF=ma in order to find the velocity and displacement vectors.
Changing the order of displacement affect the magnitude and direction?
no
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.
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.
Will changing the order of your displacements in the vector diagram affect magnitude and direction?
No, changing the order of displacements in a vector diagram does not affect the magnitude or direction of the resultant displacement. The resultant displacement depends only on the initial and final positions, not the order in which the displacements are added.
How can vectors be added in either order?
Addition is commutative, A + B = B + A.
Is the order of addition important when three or more vectors are added?
No it has no effect.
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.
How should two vectors lie so that their resultant is zero?
In order for two vectors to add up to zero:-- their directions must be exactly opposite-- their magnitudes must be exactly equal
What is another name for the third order deritative of displacement?
First derivative of displacement with respect to time = velocity. Second derivative of displacement with respect to time = acceleration. Third derivative of displacement with respect to time = jerk.
