Q: A vector may be resolved into only two components?

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A vector can have as many components as you like, depending on how may dimensions it operates in.

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.

No a vector may not have a component greater than its magnitude. When dealing with highschool phyics problems, the magnitude is usually the sum of two or more components and one component will offset the other, causing the magnitude to be less then its component

You must find the x and y components of each vector. Then you add up the like x components and the like y components. Using your total x component and total y component you may then apply the pythagorean theorem.

It is the rate of change in the vector for a unit change in the direction under consideration. It may be calculated as the derivative of the vector in the relevant direction.

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Given a vector in space, it can be resolved into any number of components based on the dimensions of the space. For 2D space, a vector can be resolved into two components (x, y), while for 3D space, it can be resolved into three components (x, y, z). Additional dimensions would result in more components needed to fully resolve the vector.

Yes, a vector in three-dimensional space can be resolved into three components along the X, Y, and Z axes. These components represent the magnitude of the vector in each respective direction. This allows for the vector's orientation and magnitude to be understood in relation to the coordinate system it is being resolved in.

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.

A vector can have as many components as you like, depending on how may dimensions it operates in.

Scalar - a variable quantity that cannot be resolved into components. Most of the physical quantities encountered in physics are either scalar or vector quantities. A scalar quantity is defined as a quantity that has magnitude only. Typical examples of scalar quantities are time, speed, temperature, and volume. A scalar quantity or parameter has no directional component, only magnitude. For example, the units for time represent an amount of time only and tell nothing of direction. Vector - a variable quantity that can be resolved into components. A vectorquantity is defined as a quantity that has both magnitude and direction. To work with vector quantities, one must know the method for representing these quantities. Magnitude, or "size" of a vector, is also referred to as the vector's "displacement." It can be thought of as the scalar portion of the vector and is represented by the length of the vector. By definition, a vector has both magnitude and direction. Direction indicates how the vector is oriented relative to some reference axis.

You can add vectors graphically (head-to-foot). Mathematically, you can add the individual components. For example, in two dimensions, separate the vector into x and y components, and add the x-component for both vectors; the same for the y-component.Here it may be useful to note that scientific calculator have a special function to convert from polar to rectangular coordinates, and vice-versa. If you RTFM (the calculator manual, in this case), it may help a lot - a vector may be given in polar coordinates (a length and an angle); using this special function on the calculator can do the conversion to rectangular (x- and y-components) really fast.

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.

To specify a vector quantity completely, you must state its magnitude (size), direction (specific orientation in space), and the coordinate system in which it is defined. Additionally, for 3-dimensional vectors, you may need to specify its components along the x, y, and z axes.

No, chickenpox is a scalar, so while it is not a vector in and of itself, it may influence other vectors such as Ebola.

Its either reality based (vertical is up-down, horizontal is ground distance) or it's purely arbitrary.

Yes, the direction of a vector can be different in different coordinate systems if the basis vectors or axes of those coordinate systems are different. The numerical components of the vector may change, affecting how it is represented, but the vector itself remains unchanged.

Vectors are added by adding the components of each vector in the same direction. For example, to add two vectors in the x-direction, you add their x-components, and for the y-direction, you add their y-components. The resultant vector is then the sum of these component-wise additions.