Why vector form is convenient?

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In summary, the vector form is a convenient way to specify a point relative to the origin in a 3D coordinate system because it contains all the necessary information without any extra details. This is important because a single number would not be enough to identify a point in a 3D space. By arranging the coordinates in an array, it is easier to interpret and perform algebraic operations on them, making them more like numbers. This is all possible because of the geometry of similar triangles and the concept of vector multiplication. Thank you to both Arildno and the other person for clarifying this doubt.
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I read that a point relative to origin in 3D coordinate system is conveniently specified by the vector form, why?
 
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Because
a) the vectorial description contains all the info required to identify the point, and nothing superfluous
b) The manner in which we write vectors makes it easy for us to treat them as a type of numbers; that is, we easily see how to add, and for that matter (sort of) multiply them together, and also how to interpret, in a geometric sense, what such algebraic operations "really" means.
 
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Because there are many different points the same distance from the origin (or anyone point) of a coordinate system so a single number will not suffice to identify it. Equivalently, it take 3 numbers to identify everypoint in a 3D coordinate system (pretty much the definition of "3D") and it is convenient to arrange those numbers in an array. It is the fact, from geometry of similar triangles, that the coordinates [itex](x_0, y_0, z_0)[/itex] of a point exactly 1/2 way between two points [itex](x_1, y_1, z_1)[/itex] and [itex](x_2, y_2, z_2)[/itex] are [itex](x_0, y_0, z_0)= ((x_1+ x_2)/2, (y_1+ y_2)/2, (z_1+ z_2)/2)[/itex] that means that "scalar multiplication" of vectors is convenient (in fact, "scalar multiplication" and the whole idea of vectors was created to simplify that).

(Arildno got in two minutes before me! And we are saying essentially the same thing.)
 
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got it, Thank you both for clarifying my doubt
 
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Vector form is convenient for specifying a point relative to the origin in a 3D coordinate system because it allows for a concise and efficient representation of the point's position in space. Unlike other forms, such as Cartesian coordinates, which require three separate values to define a point, vector form only requires a single vector with three components. This makes it easier to perform mathematical operations and transformations on the point, as well as to visualize its location in relation to other points in the coordinate system. Additionally, vector form is useful in many scientific and engineering applications, such as physics and computer graphics, where precise and efficient representation of points in space is crucial. Overall, vector form offers a convenient and versatile way to specify points in 3D coordinate systems.
 

1. Why is vector form more compact than other forms?

Vector form expresses a quantity using both magnitude and direction, allowing for a concise representation of complex information in a single mathematical expression.

2. How does vector form simplify calculations?

Using vector form allows for the use of vector operations, such as addition and multiplication, to solve problems involving multiple quantities and their directions. This simplifies calculations and reduces the number of steps needed to find a solution.

3. In what situations is vector form particularly useful?

Vector form is commonly used in physics and engineering to describe forces, velocities, and other physical quantities that involve both magnitude and direction. It is also useful in computer graphics, where it is used to represent the movement and position of objects.

4. Can vector form be applied to any type of quantity?

Vector form is most commonly used for quantities that have both magnitude and direction, such as displacement, velocity, and acceleration. However, it can also be applied to other quantities such as electric and magnetic fields, where direction is an important factor.

5. Are there any disadvantages to using vector form?

While vector form is convenient in many situations, it can sometimes be more difficult to visualize and understand compared to other forms, such as scalar form. It also requires knowledge and understanding of vector operations, which may be challenging for some individuals.

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