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Yes. There are, in fact, an infinite number of other bases in which to express a spacial vector. The rectangular coordinate basis (or Cartesian basis) is the set of unit vectors composed of a vector x pointing in an arbitrary direction from an arbitrarily chosen origin, a vector y perpendicular to x, and a vector z which is mutually perpendicular to both x and y in a direction dictated by the right-hand rule (x×y).
Another common basis is the spherical polar basis composed of the unit vectors ρ, φ, and θ where ρ points from an arbitrarily chosen origin towards the point in space one wishes to specify, φ is perpendicular to ρ, and θ is defined as φ×ρ.
There are an infinite number of other bases by which one can specify a point in space. The reason that bases such as the Cartesian basis and the spherical polar basis are seen so commonly is because they are simple and intuitive.
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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.
The process of breaking a vector into its components is sometimes called?
The process of breaking a vector into its components is sometimes called vector resolution. This involves determining the horizontal and vertical components of a vector using trigonometry or other mathematical techniques.
How many components have a vector?
It is the other way round - it's the vector that has components.In general, a vector can have one or more components - though a vector with a single component is often called a "scalar" instead - but technically, a scalar is a special case of a vector.
How do you add vectors that are perpendicular?
Vectors can be added graphically: draw one vector on paper, move the other so that its tail coincides with the head of the first. Vectors can also be added by components. Just add the corresponding components together. For example, if one vector is (10, 0) and the other is (0, 5) (those two would be perpendicular), the combined vector is (10+ 0, 0 + 5), that is, (10, 5). Such a vector can also be converted to polar coordinates, that is, a length and an angle; use the "rectangular to polar" conversion on your scientific calculator to do that.
Are rectangular components always at right angle to each other?
Not necessarily.
How do vectors add?
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.
What is the formula for finding the dimensions of a rectangular?
The word "rectangular" is an adjective, not a noun. So, a "rectangular" cannot exist. The question is like asking for the dimensions of a blue. What you need to do is specify rectangular WHAT! A rectangular pyramid, a rectangular prism, a rectangular dipyramid or some other shape.
Can the magnitude of a vector be ever equal to one of its components?
Yes. - if all the other components are zero. When the word "component" means the mutually perpendicular vectors that add (through vector addition) to form the resultant, then then answer is that "the magnitude of a vector" can equal one of its components, if and only if all other components have zero length (magnitude). This answer applies to the typical case of a vector being expressed in terms of components defined by an orthogonal basis. In normal space, these basis vectors merely define the relevant orthogonal coordinate system. There are, however, mathematical systems that use a nonorthogonal basis and the answer is different and presumably not part of the submitted question.
How can a force be resolved into its perpendicular components?
1) Graphically. Draw an arrow for the force, and measure the vertical and horizontal components. 2) Use trigonometry. The x-component is the length of the vector times the cosine of the angle, while the y-component is the length of the vector times the sine of the angle. 3) Use the polar-to-rectangular conversion on your scientific calculator. This is the fastest method, but the details are a bit complicated (since the calculator needs to return two values), and vary from one calculator to another. Check your calculator's manual.
How do you add and subtract vectors?
Graphically: By laying them head-to-tail (move one of the vectors without rotatint it, so that its tail coincides with the head of the other vector). Algebraically: Separate each vector into components, e.g. in 2 dimensions, separate it into components along the x-axis and along the y-axis. Add those components. To subtract, just add the opposite vector.
What is component method of vector vector addition?
In the component method of vector addition, vectors are broken down into their horizontal and vertical components. The horizontal components of the vectors are added together, and the vertical components are added together separately. The resulting horizontal and vertical components are then used to find the magnitude and direction of the resultant vector.
Why vector quantities cannot be added and subtracted like scalar quantities?
Mainly because they aren't scalar quantities. A vector in the plane has two components, an x-component and a y-component. If you have the x and y components for each vector, you can add them separately. This is very similar to the addition of scalar quantities; what you can't add directly, of course, is their lengths. Similarly, a vector in space has three components; you can add each of the components separately.
