we are given
equations as
[tex]x^2+y^2=64[/tex]
[tex]z=xy[/tex]
Let's assume
general form of r(t)
[tex]r(t)=x(t)i+y(t)j+z(t)k[/tex]
We can take
[tex]x(t)=8cos(t)[/tex]
[tex]y(t)=8sin(t)[/tex]
[tex](x(t))^2+(y(t))^2=(8cos(t))^2+(8sin(t))^2[/tex]
[tex](x(t))^2+(y(t))^2=64((cos(t))^2+(sin(t))^2)[/tex]
[tex](x(t))^2+(y(t))^2=64[/tex]
so, x(t) and y(t) satisfies the given equation
now, we can find z
[tex]z=x(t)y(t)[/tex]
[tex]z=8cos(t)*8sin(t)[/tex]
[tex]z=64cos(t)sin(t)[/tex]
so, we will get vector as
[tex]r(t)=(8cos(t))i+(8sin(t))j+(64cos(t)sin(t))k[/tex]................Answer
