which one of the following is the graph of the vector function r(t) = course hero

What is vector function?

Which component determines the axis that the helix rotates about?

What would happen if there was a constant in the z-z component?

How to graph a line?

What happens if we allow the coefficients on the sine and cosine for both the circle and helix?

Which axis rotates the helix?

Is position vector included in Sketch?

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Vectors - Desmos

Conic Sections: Parabola and Focus. example. Conic Sections: Ellipse with Foci

3D Vector Plotter | Academo.org - Free, interactive, education.

The demo above allows you to enter up to three vectors in the form (x,y,z). Clicking the draw button will then display the vectors on the diagram (the scale of the diagram will automatically adjust to fit the magnitude of the vectors).

3D Calculator - GeoGebra

Free online 3D grapher from GeoGebra: graph 3D functions, plot surfaces, construct solids and much more!

Graphing Calculator - Desmos

Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.

What is vector function?

A vector function is a function that takes one or more variables and returns a vector. We’ll spend most of this section looking at vector functions of a single variable as most of the places where vector functions show up here will be vector functions of single variables.

Which component determines the axis that the helix rotates about?

As with circles the component that has the t t will determine the axis that the helix rotates about. For instance,

What would happen if there was a constant in the z-z component?

If this one had a constant in the z z component we would have another circle. However, in this case we don’t have a constant. Instead we’ve got a t t and that will change the curve. However, because the x x and y y component functions are still a circle in parametric equations our curve should have a circular nature to it in some way.

How to graph a line?

To graph this line all that we need to do is plot the point and then sketch in the parallel vector. In order to get the sketch will assume that the vector is on the line and will start at the point in the line. To sketch in the line all we do this is extend the parallel vector into a line.

What happens if we allow the coefficients on the sine and cosine for both the circle and helix?

Also note that if we allow the coefficients on the sine and cosine for both the circle and helix to be different we will get ellipses.

Which axis rotates the helix?

will be a helix that rotates about the y y -axis and is in the shape of an ellipse.

Is position vector included in Sketch?

Note however, that in practice the position vectors are generally not included in the sketch.

What is vector function?

A vector function is a function that takes one or more variables and returns a vector. We’ll spend most of this section looking at vector functions of a single variable as most of the places where vector functions show up here will be vector functions of single variables.

Which component determines the axis that the helix rotates about?

As with circles the component that has the t t will determine the axis that the helix rotates about. For instance,

What would happen if there was a constant in the z-z component?

If this one had a constant in the z z component we would have another circle. However, in this case we don’t have a constant. Instead we’ve got a t t and that will change the curve. However, because the x x and y y component functions are still a circle in parametric equations our curve should have a circular nature to it in some way.

How to graph a line?

To graph this line all that we need to do is plot the point and then sketch in the parallel vector. In order to get the sketch will assume that the vector is on the line and will start at the point in the line. To sketch in the line all we do this is extend the parallel vector into a line.

What happens if we allow the coefficients on the sine and cosine for both the circle and helix?

Also note that if we allow the coefficients on the sine and cosine for both the circle and helix to be different we will get ellipses.

Which axis rotates the helix?

will be a helix that rotates about the y y -axis and is in the shape of an ellipse.

Is position vector included in Sketch?

Note however, that in practice the position vectors are generally not included in the sketch.