Respuesta :

Answer:

r(t) = 6 cos ti + 6 sin tj + (36 cos t sin t)k

Step-by-step explanation:

Given that

[tex]x^2 + y^2 = 36\ i.e. 6^2[/tex]

And,

z = xy

Now the general form is

r(t) = x(t) i + y(t) j + z(t) k

Now take

x (t) = 6 cos t

And, y (t) = 6 sin t

So,

[tex]x^2 + y^2 = 6^2 cos^2t + 6^2 sin^2 t\\\\= 6^2 (cos^2t + sin^2t)\\\\=6^2\\\\= 36[/tex]

So,

x (t) = 6cost t

And, y (t) = 6 sin t

this satisfied the

[tex]x^2 + y^2 = 36[/tex]

Now

z = xy

= 6cos t × 6 sin t

= 36 cos t sin t

Therefore,

r(t) = 6 cos ti + 6 sin tj + (36 cos t sin t)k

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