Multivariable Calculus Maple Help

[Mbruinsma]

1. I am working on an assignment in maple for my Calc 3 class. It seems really simple, but I have no experience using Maple. Any help would be very much appreciated.

PART 1: 3D – VECTORS IN MAPLE
1. Let u= i + 2j. Define a vector v. Draw the two vectors in a Maple graph.
2. Use Maple to compute the dot product of u and v.
3. Use Maple to compute the length of both vectors without using a formula that involves the vector components.
4. Using 2 and 3, write a formula for computing the angle between u and v.
5. Use the formula to compute the angle in radians, and also in degrees.
6. Find a vector w that is perpendicular to v. Use Maple to prove that w and v are perpendicular.
7. Graph both vectors in Maple to visualize that the angle between them is a right angle.



I started by setting u:=([1,2]). I then made a vector v:=([2,1]) (Does it matter what vector I use? I just chose 2i+j) How can I graph this and how do I do the dot product?

Thanks for Any help you can give me!

 

[LCKurtz]

1. I am working on an assignment in maple for my Calc 3 class. It seems really simple, but I have no experience using Maple. Any help would be very much appreciated.

PART 1: 3D – VECTORS IN MAPLE
1. Let u= i + 2j. Define a vector v. Draw the two vectors in a Maple graph.
2. Use Maple to compute the dot product of u and v.
3. Use Maple to compute the length of both vectors without using a formula that involves the vector components.
4. Using 2 and 3, write a formula for computing the angle between u and v.
5. Use the formula to compute the angle in radians, and also in degrees.
6. Find a vector w that is perpendicular to v. Use Maple to prove that w and v are perpendicular.
7. Graph both vectors in Maple to visualize that the angle between them is a right angle.






I started by setting u:=([1,2]). I then made a vector v:=([2,1]) (Does it matter what vector I use? I just chose 2i+j) How can I graph this and how do I do the dot product?

Thanks for Any help you can give me!

Unfortunately for you, it depends on what version of Maple you are using. Here are some steps that work in Maple 13, which may or may not help you. You might have to refer to your class lessons

> with(VectorCalculus); BasisFormat(false);
> u := <1|2>;
v := `<3|5>;
> v.u;
> Norm(u, 2);
> PlotVector(u, scaling = constrained);
>

 

[Mbruinsma]

Thank you so much for your help LCKurtz. I am using Maple 13.

 

[Mbruinsma]

This is the next part. If anyone can give me any tips on getting started, I'd appreciate it.

Thanks!

PART 2: CURVATURE OF THE GRAPH OF A VECTOR VALUED FUNCTIONS
The curvature function of this space curve is constructed via the following formula:

1. Let r(t) = (cost, sint). Graph in maple r(t) for 0<t<2п.
2. Write in maple, in vector form r’(t) and r’’(t).
3. Using Maple to compute the cross product of r’(t) and r’’(t)
4. Using Maple to compute the length of the vector resulting from 2.
5. Using maple compute the length of r’(t) and the cube it.
6. Compute the funtion K(t). You should not find this result surprising, why?
7. Use the observation in 5. to decide what should the curvature of a circle with radius r is.
8. Repeat all the process from 1 to 7 to find the curvature function of a given ellipsis. Compare the curvature function of an ellipses with the curvature funtion of a circle.
9. Repeat all the process from 1 to 7 to find the curvature function of a 3D vector valued funtion. Be creative or choose any vector valued function given in the textbook.I can't seem to graph r(t). I don't know why.

 

[LCKurtz]

For cross products, you will need 3D vectors:

> with(plots):
> r := <cos(t)|sin(t)|0>;
> spacecurve(r, t = 0 .. 2*Pi, axes = boxed, color = black);