Practice question · Multiple choice
The gradient of a scalar field points in the direction of steepest increase. Why is it perpendicular to the level surfaces?
Hints
- What is the rate of change AS you walk along a contour line?
- Write that as a dot product with the gradient.
Show the answer
D. Because moving along a level surface changes nothing
Why
Zero change along the surface forces a zero dot product. This is why a contour map shows the steepest route as the one crossing contours at right angles.
Practise Gradient, Divergence, and Curl
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