Calc III Review
Graphing in 3D
In the three-dimensional coordinate system, the -axis is red, the -axis is green, and the -axis is blue.
In the coordinate system below, graph the point (-1, 2, 3)
Since the -plane is the one that is flat, we can number those quadrants as we would in a 2D graph. After you graphed the point, you observed that the point lies above quadrant 2 of the -plane.
Based on this information, answer the question below the graphing window
3D Graph
Location of point in 3D
The point, (4,-3,-2) would land below which quadrant in the -plane?
Vector Basics
To create a vector with initial point at the origin and coordinates ending at the point (1,2,3), type Vector ((1,2,3)) into the Input bar. You will notice that Geogebra automatically names your vector, u, v, etc. This is helpful later on when you want to use other commands with these vectors.
To create a vector with initial point at (1,2,3) and terminal point at (-3,4,5), type Vector((1,2,3),(-3,4,5)).
To find the magnitude of a vector, u, type abs(u). Abs is an abbreviation for absolute value.
To find the dot product of two vectors, use the asterisk key on your keyboard, type u*v.
To find the cross product of two vectors, type Cross(u,v).
Below in the 3D window, sign in to your Geogebra account. Then create the following vectors, u = (-3, 1, 5) and v = (2, -4, -1). Then in the same window, perform the following commands: abs(u), u + v, v - u, the dot product of u and v, and the cross product of u and v.
3D Graph
Magnitude of a vector
Write the definition of the magnitude of a vector. You may use Google if you do not know the answer.
Dot product of two vectors
Write the definition of the dot product of two vectors. You may use Google if you do not know the answer.
Cross product of two vectors
Write the definition of the cross product of two vectors. You may use Google if you do not know the answer.
Graphing Surfaces
To graph a surface in Geogebra 3D, you simply type the equation of the surface in the Input bar. Geogebra will automatically assign a function name to the surface.
In the Input bar, type cos(y) + cos(z).
Now use your mouse to rotate the surface so that you can see that there are several relative maxima and minima.
Plot points at two of the local maxima. HINT: the x-coordinate is
Plot points at two of the local minima.
3D Graph
Local Maxima
There are infinitely many local maxima. Write a formula to represent all of the points where the local maxima occur.
Local Minima
There are infinitely many local minima. Write a formula to represent all of the points where the local minima occur.