Answer: (a) r1(t) = <2cost , 0 , 2sint>
(b) <2cost , (1 - 12sint - 10cost)/8 , 2sint>
Step-by-step explanation:
x2+z2=4
a)
Now, in the xz plane, we know that y = 0...
So, x^2 + z^2 = 4 will simply be a circle centered at (0,0)..
This can be easily parameterized as
x = 2cos(t)
z = 2sin(t)
So, the required parameterization is :
r1(t) = <2cost , 0 , 2sint>
b)
Cylinder : x^2 + z^2 = 4
Plane : 5x+8y+6z=1
Easily enough, the x^2 + z^2 = 4 can again be parameterized as
x = 2cost , z = 2sint
With this, we can find y using plane equation...
5x+8y+6z=1
5(2cost) + 8y + 6(2sint) = 1
8y = 1 - 12sint - 10cost
y = (1 - 12sint - 10cost)/8
So, the parameterization is :
<2cost , (1 - 12sint - 10cost)/8 , 2sint>
