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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.
What else can I help you with?
What is the angle between the rectangular components of a vector?
The angle between the rectangular components of a vector can be found using the arctangent function. If a vector has components (A_x) (horizontal) and (A_y) (vertical), the angle (\theta) between the vector and the horizontal axis is given by (\theta = \tan^{-1}\left(\frac{A_y}{A_x}\right)). The components themselves are at right angles (90 degrees) to each other, as they are defined along perpendicular axes.
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.
Is A plus B equals 0 what can you say about the components of the two vectors?
If A + B = 0, this means that vector A is equal in magnitude but opposite in direction to vector B. In other words, the two vectors are anti-parallel to each other. This relationship indicates that the components of the two vectors cancel each other out when added together, resulting in a net vector of zero.
Are rectangular components always at right angle to each other?
Not necessarily.
How do vectors add?
To add vector A and vector B: Take the x- and y-components of vectors A and B; to find the components, use trig or the properties of right triangles, or your vectors may be given in coordinate (x,y) form already. Add the x-components and the y-components. The respective sums are the components of the new vector. For example: vector A = (-5, 10), vector B = (1, 2) -5+1= -4 --> x-component of new vector 10+2= 12 --> y-component of new vector Resultant vector = (-4, 12) Different setup: vector A = magnitude 10 at angle 30 degrees off horizontal vector B = magnitude 5 at angle 150 degrees off horizontal A = (10cos30, 10sin30) = (Ax, Ay) B = (5cos150. 5sin150) = (Bx, By) Compute Ax, Ay, Bx, By using calculator or unit circle. Add Ax + Bx = Cx Add Ay + By = Cy New vector coordinates are (Cx, Cy) If you need the magnitude, take sqrt( Cx^2 + Cy^2). For the angle, take arctan( Cy/Cx). There are other setups where the angle is off the vertical- in this case, switch the sin, cos functions to find your components for that vector. My best advice would be to draw the problem, and use what you know about right triangles. Good luck!!
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.
