## Question

###### U(x,Y, 2) is a scalar field_ How is the directional derivative dU/ds related to VU? Unit vector d lies along the line x/3-y/4-2/5, pointing away from the origin: Find d_ and hence find the directional derivative of U = x2+y2+z2 at the point [1,2,3] along & Find the maximum rate of increase of U with respect to distance at the point [1,2,3]. Show that VU is perpendicular to any surface U-constant_ Find the unit normal to the level surfaces of U x2 y2 + 22 in the direction of increasing U at t

U(x,Y, 2) is a scalar field_ How is the directional derivative dU/ds related to VU? Unit vector d lies along the line x/3-y/4-2/5, pointing away from the origin: Find d_ and hence find the directional derivative of U = x2+y2+z2 at the point [1,2,3] along & Find the maximum rate of increase of U with respect to distance at the point [1,2,3]. Show that VU is perpendicular to any surface U-constant_ Find the unit normal to the level surfaces of U x2 y2 + 22 in the direction of increasing U at the point [1,2,3].

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