A smooth curve is normal to a surface ƒ(x, y, z) = c at a point of intersection if the curve’s velocity vector is a nonzero scalar multiple of ∇ƒ at the point. Show that the curve r(t) = sqrt(t) i + sqrt(t) j-1/4(t+3)k is normal to the surface x2 + y2 - z = 3 when t = 1.

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.