Practice question · Fill in the blanks
Complete the following passage by choosing the correct terms from the word bank.
The magnitude |rᵤ ᵥ| gives the local ______ of the surface element, and its direction gives the surface ______.
Word bank: area · normal · tangent · curvature
Hints
- The two tangent vectors come from differentiating the parametrisation.
- Their cross product supplies both direction and area scaling at once.
Show the answer
The magnitude |rᵤ ᵥ| gives the local area of the surface element, and its direction gives the surface normal.
Why
The cross product of tangent vectors gives the normal with magnitude = area element.
Practise Surface Integrals
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