Let $S$ be the surface of a sphere centered at the origin that is missing its top. Its boundary curve is $C$. The normal of $S$ is defined by the arrow pointing upward from its base.

What is the positive orientation of $C$ with respect to $S$ ?

Choose 1 answer:
(A) Clockwise
(B) Counterclockwise

Question

Let $S$ be the surface of a sphere centered at the origin that is missing its top. Its boundary curve is $C$. The normal of $S$ is defined by the arrow pointing upward from its base.

What is the positive orientation of $C$ with respect to $S$ ?

Choose 1 answer:
(A) Clockwise
(B) Counterclockwise

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine the positive orientation of curve $C$ with respect to surface $S$, we need to apply the right-hand rule. ‖ ‖ step 2 ⋮ Point the thumb of your right hand in the direction of the normal vector of $S$, which is upward as indicated by the red arrow in the image. ‖ ‖ step 3 ⋮ The fingers of your right hand will curl in the direction of the positive orientation of curve $C$. ‖ ‖ step 4 ⋮ Since the normal vector points upward, the fingers curl in the counterclockwise direction when viewed from above. ‖ ∻1 Answer∻ ***B*** ∻Key Concept∻ ⚹Right-hand rule for positive orientation⚹ ∻Explanation∻ ⚹The right-hand rule is used to determine the direction of the positive orientation of a curve with respect to a surface normal.⚹◊What is the relationship between the boundary curve $C$ and the surface $S$ in a three-dimensional geometric figure?⍭ Generate me a similar question◊

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