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Vectros can come in any number of components when the component reflects a dimension. Vectors reflect dimensionality of the space. If the problem has three dimensions, three components are enough, two components are insufficient to handle the problem and 5 dimensions may be too much.
Operations are also importnat, not just number of components. Only a few vector spaces provide division. if your problem needs division, 3 and 5 dimension vectors are not capable of division algebra. Only 1,2,4 dimension spaces have associative division algebras.
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Vector may be resolved into only three components?
A vector may be represented as a combination of as many components as you feel would satisfy you, without limit. Whatever ludicrous quantity you choose, for whatever private reason, a group of that many vectorlets can always be defined that combine to have precisely the magnitude and direction of the original single vector. Even though this fact is worth contemplating for a second or two, it's generally ignored, mainly because it is so useless in the practical sense ... it doesn't make a vector any easier to work with when it is replaced by 347 components, for example. The most useful number of components is: one for each dimension of the space in which the original vector lives. Two components to replace a vector on a flat graph, and three components to replace a vector in our world.
What is component method of vector vector addition?
Any vector could be resolved into perpendicular components one along x axis and the other along y axis. So all vectors would be split into two components. Now we can easily add the x components and y components. If all in the same simply addition. If some are in opposite we have to change its sign and add them. Finally we will have only two one along x and another along y. Now we can get the effective by using Pythagoras.
It is possible for a vector to be zero if a component of the vector is not zero?
No. The value of a vector is determined by the square root of the sum of its components squared. Value= Sqrt(x^2 + y^2 + z^2). The components of real vectors are real numbers and the square of a real number is a positive number. The sum of a positive and zeros is not zero but a positive. Vectors were created by William Rowan Hamilton in 1843 when he created Quaternions. Quaternions consist of a real number and three vector numbers. The vectors are designated by i, j, k where i^2=j^2=k^2=ijk= -1. The square of a vector is a negative one . This used to be called an imaginary number. The components of vectors are real numbers, like v=2i + 3j -5k, the value of v = sqrt(4 + 9 + 25)=sqrt(38). Complex numbers are a subset of quaternions involving one vector "i".
How do vectors add?
Just add their magnitudes. The combined vector will have the same direction as the original vectors.Just add their magnitudes. The combined vector will have the same direction as the original vectors.Just add their magnitudes. The combined vector will have the same direction as the original vectors.Just add their magnitudes. The combined vector will have the same direction as the original vectors.
What is a perpendicular vector?
"Perpendicular " is a relationship, not a vector. Any vector can be perpendicular to any other vector if their angle relationship is an odd multiple of 90 degrees.
What is the sum of two or more vectors added together called?
The sum of any number of vectors is itself a vector, just as the sum of any number of scalars (normal numbers) is a normal number.If a vector is resolved into 2 components, x and y, in the form [x,y], then it can be added to any other vector resolved into 2 components [z,a].[x,y]+[z,a]=[x+z,y+a]
What is the maximun no of components into which a vector can be split?
There is no maximum. A vector can be defined for a hyperspace with any number of dimensions. Such a hyperspace can be described using an orthogonal system of axes and the vector can be split into its components along each one of these axes.
Vector may be resolved into only two components?
A vector may be represented as a combination of as many components as you feel would satisfy you, without limit. Whatever ludicrous quantity you choose, for whatever private reason, a group of that many vectorlets can always be defined that combine to have precisely the magnitude and direction of the original single vector. Even though this fact is worth contemplating for a second or two, it's generally ignored, mainly because it is so useless in the practical sense ... it doesn't make a vector any easier to work with when it is replaced by 347 components, for example. The most useful number of components is: one for each dimension of the space in which the original vector lives. Two components to represent a vector on a flat graph, and three components to represent a vector in our world.
Vector may be resolved into only three components?
A vector may be represented as a combination of as many components as you feel would satisfy you, without limit. Whatever ludicrous quantity you choose, for whatever private reason, a group of that many vectorlets can always be defined that combine to have precisely the magnitude and direction of the original single vector. Even though this fact is worth contemplating for a second or two, it's generally ignored, mainly because it is so useless in the practical sense ... it doesn't make a vector any easier to work with when it is replaced by 347 components, for example. The most useful number of components is: one for each dimension of the space in which the original vector lives. Two components to replace a vector on a flat graph, and three components to replace a vector in our world.
Can a vector has componentsgreater than the vector magnitude?
No, a vector can not have any components greater than itself.
What is component method of vector vector addition?
Any vector could be resolved into perpendicular components one along x axis and the other along y axis. So all vectors would be split into two components. Now we can easily add the x components and y components. If all in the same simply addition. If some are in opposite we have to change its sign and add them. Finally we will have only two one along x and another along y. Now we can get the effective by using Pythagoras.
Can a unit vector have any components with magnitude greater than unity?
No, by definiton, a unit vector is a vector with a magnitude equal to unity.
What is the angle between the components of a vector 0 or 90?
If a vector is broken up into components the angle between the components is 90 degrees.
What does rectangular component of a vector mean?
Any vector can be "decomposed" into components along any two non-parallel directions. In particular, a vector may be decomposed along a pair (more in higher dimensional spaces) of orthogonal directions. Orthogonal means at right angles and so you have the original vector split up into components that are at right angles to each other - for example, along the x-axis and the y-axis. These components are the rectangular components of the original vector. The reason for doing this is that vectors acting at right angles to one another do not affect one another.
Can you add 0 to a null vector?
Yes, any number can be added to a null vector.
What is the vector equation for the x axis?
ki where i is the unit horizontal vector, and k is any number.
It is possible for a vector to be zero if a component of the vector is not zero?
No. The value of a vector is determined by the square root of the sum of its components squared. Value= Sqrt(x^2 + y^2 + z^2). The components of real vectors are real numbers and the square of a real number is a positive number. The sum of a positive and zeros is not zero but a positive. Vectors were created by William Rowan Hamilton in 1843 when he created Quaternions. Quaternions consist of a real number and three vector numbers. The vectors are designated by i, j, k where i^2=j^2=k^2=ijk= -1. The square of a vector is a negative one . This used to be called an imaginary number. The components of vectors are real numbers, like v=2i + 3j -5k, the value of v = sqrt(4 + 9 + 25)=sqrt(38). Complex numbers are a subset of quaternions involving one vector "i".
