Find a vector-valued function whose graph is the ellipsoid .

Question

Find a vector-valued function whose graph is the ellipsoid  .

Quizplus · Accepted Answer

The equation of the ellipsoid is given by:

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

Thus, one possible vector-valued function whose graph is the ellipsoid is:

r(t) = <3cos(t), 2sin(t), sin(t)>

Then,

x(t) = 3cos(t)
y(t) = 2sin(t)
z(t) = sin(t)

and the equation of the ellipsoid becomes:

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

which is true for all t. Therefore, the correct choice is C.

Find a Vector-Valued Function Whose Graph Is the Ellipsoid