. Find a vector function that represents the curve of intersection of the surfaces x^2+y^2 = 8and z = 3xy + 7:

aruv | Student

Let x=t , substitute x in one equation of the curve

`t^2+y^2=8`

`y^2=8-t^2`

`y=sqrt(8-t^2)`      (ii)

Substitute x and y in another equation of the given curve.

`z=3tsqrt(8-t^2)+7`

Thus  `(t,sqrt(8-t^2),3tsqrt(8-t^2)+7)`  is the required vector function.