Every question below has an applet below for you to use as you experiment with the 3-Dimensioanl space. [br]Once you have answered the question, you may click on "Check My Answers" to see the correct responses.
What is the equation of the [i]xy[/i]-plane in the Three Dimensional Space? What about the [i]zy-[/i]plane?
What does the graph of x=2 look like when viewed on a number line (Singular Dimension)?
A single point with x-coordinate of 2.
What does the graph of x=2 look like when viewed in the 2 Dimensional Cartesian plane?
A vertical line passing through the point (2,y), where y is any real number.
What does the graph of x=2 look like when viewed in 3 dimensions?
A plane parallel to the [i]yz-[/i]plane.
[list=1][*]What’s the equation of a plane [i][b]parallel [/b][/i]to the[i][b] xy-plane[/b][/i] and contains the point (3, 4, 8)?[/*][*]What’s the equation of a plane [i][b]parallel [/b][/i]to the [b][i]xz-plane[/i][/b] and contains the point (1, 6, 5)?[/*][*]What's the equation of a plane [i][b]perpendicular [/b][/i]to the [i][b]yz-plane[/b][/i] and contains the point (1, 6, 5)[/*][*]What's the equation of a plane [i][b]perpendicular [/b][/i]to the [i][b]xz-plane[/b][/i] and contains the point (1, 6, 5)?[/*][/list][br][br]
[list=1][*]z = 8[/*][*]y = 6[/*][*]y = 6 or z=5[/*][*]x=1 or z=5[/*][/list]
What does the graph of [math]x^2+y^2=16[/math] look like when viewed in the Cartesian plane?
A circle, centered at the origin, with a radius of 4.
Describe the graph of [math]f\left(x\right)=sin\left(x\right)[/math] in the Cartesian Plane.
A sinusoidal curve passing through the origin, with a its first maximum at [math]x=\frac{\pi}{2}[/math] and first minimum at [math]x=\frac{3\pi}{2}[/math]. The graph has a period of [math]2\pi[/math] and an amplitude of 1.
The last two graphs you described are created in the Cartesian plane, in other words, they are 2-dimensional. What do the same graphs look like when examined in 3 dimensions? [br]Make your conjectures and test them using the applet below.
Use the applet below to find for yourself.
Describe the intersection of [math]x^2+y^2=9[/math] and [math]z=5[/math].
Circle centered at (0,0,5) with a radius of 3 and contained in the plane z=5.
Describe the graph of each of the following[br][list=1][*][math]x^2+y^2+z^2=9,z\le0[/math][br][/*][*][math]x^2+y^2+z^2\le9[/math][br][/*][*][math]x^2+y^2+z^2<9[/math][br][br][br][/*][/list]
[list=1][*]Lower half of a sphere centered at the origin with a radius of 3.[/*][*]The solid ball bounded by the sphere [math]x^2+y^2+z^2=9[/math][br][/*][*]The interior of the sphere [math]x^2+y^2+z^2=9[/math][/*][/list]
Find the equation(s) for a circle with radius 3 centered at [math]\left(-2,5,1\right)[/math] and lying in a plane parallel to the [i]yz[/i]-plane.
[math]\left(y-5\right)^2+\left(z-1\right)^2=9,x=-2[/math]
Find the equation(s) of a with radius 2 centered at [math]\left(-2,6,-3\right)[/math] and lying in a plane perpendicular to the [i]xz-[/i]plane.
[math]\left(x+2\right)^2+\left(y-6\right)^2=4,z=-3[/math]