I can figure out how to plot this for calc 3.

question:

a) Plot the circle of radius 3 centered at the point {-1, 1, 1} in the plane whose xyz-equation is 2(x + 1) + 3(y - 1) + (z - 1) = 0. Include in your plot a big enough piece of the plane to accommodate the circle.

My answer: Given;

Radius = 3 Center = {-1, 1, 1}

2(x + 1) + 3(y - 1) + (z - 1) = 0

2x + 2 + 3y - 3 + z - 1 = 0

2x + 3y + z = -2 + 3 + 1

2x + 3y + z = 2

Normal = {2, 3, 1}

Equation of line:

r(t) = {-1, 1, 1} + t {2, 3, 1}

equation of plane:

2x + 3y + z = 2 (divide by 2) (2x + 3y + z )/ 2 = 2/2

(x + 3y/2 + z/2 ) = 1

x intercept = 1

y intercept = 2/3

z intercept = 2

How do I plot this???

b) Here's a plot of a spiral in the xy-plane: Clear[spiral, t]; spiral[t_] = {t Cos[2 t], t Sin[2 t]}; ParametricPlot[spiral[t], {t, 0, 3 Pi}, AxesLabel -> {"x", "y"}]

Use your answer to part a) above to help plot a true scale duplicate copy of this spiral on the plane with xyz-equation 2(x + 1) + 3(y - 1) + (z - 1) = 0. Center your spiral at {-1, 1, 1} and include in your plot a big enough hunk of the plane to accommodate the spiral.

annnnd how do I plot this?

Thanks!!