The surface S is defined by x + y² + z³ = 3. Find a vector normal to S at the point A with position vector a = (1, 1, 1).

Q: Parametrize the line that passes through the point (1,2,3) parallel to the vector v = -3i + 7k.

A:

Q: Let C = (-2, -1) be the center of dilation. Let X = (1, 1), Y = (3, 0) and Z = (2,5). Our dilation…

A: Center of dilation=-2, -1X=1, 1, Y=3, 0, Z=2, 5Dilation factor, k=3

Q: 2. Find a vector that is perpendicular to the surface x² + y² + z² = xyz + 8 at the point (1,2,3).

A: Given that x²+y²+z²=xyz+8 At (1,2,3)

Q: Consider the plane x-y-z-8= 0. Find the point in this plane closest to the point (1, 0, 1).

A: