In the three-dimensional coordinate system, the [math]x[/math]-axis is red, the [math]y[/math]-axis is green, and the [math]z[/math]-axis is blue.[br][br]In the coordinate system below, graph the point (-1, 2, 3)[br][br]Since the [math]xy[/math]-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 [math]xy[/math]-plane.[br][br]Based on this information, answer the question below the graphing window

To create a vector with initial point at the origin and coordinates ending at the point (1,2,3), [b]type Vector ((1,2,3)) into the Input bar[/b]. 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.[br][br]To create a vector with initial point at (1,2,3) and terminal point at (-3,4,5), type [b]Vector((1,2,3),(-3,4,5))[/b].[br][br]To find the magnitude of a vector, u, [b]type[/b] [b]abs(u)[/b]. Abs is an abbreviation for absolute value.[br][br]To find the dot product of two vectors, use the asterisk key on your keyboard, [b]type u*v[/b].[br][br]To find the cross product of two vectors, [b]type Cross(u,v)[/b].[br][br][b]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.[/b]

[b]To graph a surface in Geogebra 3D, you simply type the equation of the surface in the Input bar.[/b] Geogebra will automatically assign a function name to the surface.[br][br]In the Input bar, [b]type cos(y) + cos(z)[/b].[br][br]Now use your mouse to rotate the surface so that you can see that there are several relative maxima and minima.[br][br][b]Plot points at two of the local maxima. HINT: the x-coordinate is [/b][math]0.[/math][br][br][b]Plot points at two of the local minima.[/b]