Gradient vectors on a contour diagram

The image below shows a contour diagram for a function f(x,y) of two variables with a number of points scattered over the diagram. For each of the indicated points, draw the gradient vector emanating from that point. Be sure to pay attention to the direction and relative magnitude of your vectors.

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To answer this question, you should print out the diagram, draw your gradients on your printout, scan or snap a photo of you drawing, and upload that image.

How do you do the relative magnitudes?

@myost The closer the contours are together, the steeper the surface is in the direction perpendicular to those lines and, therefore, the longer the gradient vectors.

@fcarrill Three comments:

• The gradient vectors don’t necessarily point right at a max or min; rather, they should always be perpendicular to the contours at the point where you’re drawing them from.
• The gradients should generally point from darker to lighter. For example, the gradients at the dark loop on the left should be pointing away from the center - not towards it.
• The closer the contours, the longer the gradient vectors. For example, the vectors starting furthest to the right (there are two of them; one starting kinda near the top and the other kinda near the bottom) should be the shortest vectors you draw.

@roverhol OK, this is definitely an improvement over the previous post.

But, vectors tend be perfectly straight.

Much better - yes. Just be sure to draw your gradients perpendicular to the contours. My only minor complaint is that they don’t all look quite perpendicular - like the two I’ve circled here:

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