Suppose a velocity field given as V = ti+2t² j, where Cartesian coordinate and t is the time. We look at a fluid p Calculate its position when t = 3. What is the relation bet O (0,0), a parabolic curvey ~ ² O(,18), a straight line y ~ x O(2, 18), a curve satisfying y~ x O (3, 18), a parabolic curve y~ 2 49

Find equations of the tangent plane and normal line to the surface x=6y^2+5z^2−459 at the point (2, 6, 7).Equation of the tangent plane (make the coefficient of x equal to 1): =0.Vector equation of the normal line: l(t)=⟨2,,  ⟩+t⟨1, ,  ⟩.HINT. Represent the given surface as a level surface of a certain function f(x,y,z), that is, re-write the equation of the surface in the form �(�,�,�)=c, where �(�,�,�) is a function of 3 variables and f is a constant. Then find the gradient vector of the function f at the given point. The tangent plane to the surface at that point is orthogonal to the gradient vector, and the normal line -- parallel to it. This allows us to write the equations of both tangent plane and normal line.

Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 5x² - 3xy + xyz (a) Find the rate of change of the potential at P(5, 2, 5) in the direction of the vector v = i + j - k. (b) In which direction does V change most rapidly at P? 73°F Mostly cloudy (c) What is the maximum rate of change at P? Need Help? Read It Show My Work (Optional)? Watch It Q

please all parts