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Vector Function Grapher Calculator + Online Solver With Free Steps

A Vector Function Grapher Calculator is a simple online application that provides a graphical representation of Vector Functions with a domain of fundamental values and a range of vectors.

Using this calculator, you may consistently demonstrate a vector function’s spread.

What Is a Vector Function Grapher Calculator?

The Vector Function Grapher Calculator is an online tool that provides a visual depiction of the vector function at each instant in time.

A Vector Function, often known as a Vector-Value Function, is a function with a domain of all real numbers (R) and a wide range of vectors.

The vector functions ‘r’ with three-dimensional (3D) vector values are particularly important to us. This indicates that a distinct vector in V3 with the symbol ‘r’ exists for each number (t) in the r(t) range.

If the functions ‘f(t)’, ‘g(t)’, and ‘h(t)’ are real-valued functions known as the component functions of ‘r’, then they are the constituents of the vector ‘r(t)’ and we may write them as:

\[ r(t) = 〈f(t), g(t), h(t)〉 = f(t) i + g(t) j + h(t) k \]

Since time is typically represented by the character ‘t’ in vector function applications, we utilize that letter to stand in for the independent variable.

How To Use a Vector Function Grapher Calculator

You can use the Vector Function Grapher Calculator by following the given guidelines; the calculator will surely provide you with the desired results. You can therefore follow the given instructions to get the desired output.

Step 1

Enter the parametric equations of a vector in the provided entry boxes.

Step 2

Press the “Submit” button to calculate the Vector Function Plot for the given parametric equations and to view the detailed, step-by-step solution for the Vector Function Plot Calculation.

How Does a Vector Function Grapher Calculator Work?

The Vector Function Grapher Calculator works by deducting the starting point’s waypoints from the ending point’s coordinates.

Remember that the magnitude and orientation of a plane vector are the two elements. We eventually particular the second location if we go in a certain orientation for a specific distance from any point in the plane (the original point).

This is a representation of the vector’s ending point. By deducting the waypoints of the starting position from the coordinate values of the ending point, we may get the constituents of the vector.

If the starting point of a vector is at the center, it is regarded as being in the standard position. In order to ensure the graph’s distinctiveness while plotting a vector-valued function, we normally plot the vectors in the function’s range in a normal position.

The graphs of 3-dimensional (3D)  vector-valued functions also follow this approach. A vector-valued function’s graph with the following form

\[ r(t)=f(t) \hat{\mathbf{i}}+g(t) \hat{\mathbf{j}} \]

is a path that is made up of a set of all endpoints (f(t),g(t)), and the pathway is known as a plane curve. A vector-valued function’s graph with the following form

\[ r(t)=f(t)\hat{\mathbf{i}}+g(t) \hat{\mathbf{j}}+h(t) \hat{\mathbf{k}} \]

includes the collection of all coordinates f(t), g(t), and h(t), and the trajectory it takes is referred to as a space curve. A vector mathematical model of the curve depicts a plane or space curve via a vector-valued function.

Every plane curve and space curve has a direction that, as the magnitude of the parameter t rises, indicates the direction of travel along the curve. This orientation is denoted by arrows sketched on the curve.

The parameter is subject to the constraint if the range of values of t is constrained to the constants in the interval [a,b].

The parameterized function’s graph and the vector-valued function’s graph would then be in agreement, with the vector-valued graph representing vectors instead of points.

Solved Examples

Let’s explore some examples better to understand the workings of the Vector Function Grapher Calculator.

Example 1

Create a graph for each of the vector functions listed below.

\[ \vec r ( t ) = \langle {t,1} \rangle \]

Solution

Our first task is to enter a few t values to get some position vectors. Here are a couple:

\[ \vec r ({ – 3}) = \langle { – 3,1} \rangle \; \; \; \; \vec r ( { – 1} ) = \langle { – 1,1} \rangle \; \; \; \; \vec r  ( 2 ) = \langle {2,1} \rangle \; \; \; \; \vec r ( 5) = \langle {5,1} \rangle \]

The following points are all on the graph of this vector function, which tells us.

\[ ( { – 3,1})\; \; \; \; ( { – 1,1}) \; \; \; \; ( {2,1}) \; \; \; \; ( {5,1}) \]

Example 2

Create a graph for each of the vector functions listed below.

\[ \vec r ( t ) = \langle {t,{t^3} – 10t + 7}\rangle \]

Solution

Here are some examples of how this vector function has been evaluated.

\[ \vec r( { – 3} ) = \langle { – 3,10} \rangle \; \; \; \;\vec r( { – 1} ) = \langle { – 1,16} \rangle \; \; \; \;\vec r( 1 ) = \langle {1, – 2} \rangle \; \; \; \;\vec r( 3 ) = \langle {3,4} \rangle \]

So, the graph of this function shows us a few points. Contrary to the prior section, there aren’t really going to be enough points to understand this graph well.

In general, it may take several function evaluations to understand the graph, and it is frequently simpler to utilize a machine to create the graph.

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