Skip to main content\(\newcommand{\R}{\mathbb{R}}
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A three dimensional plot of a curved surface shown in gray above a set of axes labeled
\(x\text{,}\) \(y\text{,}\) and
\(z\text{.}\) The gray surface decreases as either x or y is increased from a maximum near the z-axis. An arrow is shown below the surface on the xy-plane in red. A line segment is shown in red on the xy-plane in same direction as the arrow and extends past the end of the arrow. This arrow is labeled with
\(\langle u_1,u_2 \rangle\) while pointing in the direction of the x and y axes. A blue plane is shown extending from the red line segment parallel to the z-axis, through the surface. The curve along the surface that is above the red segment and is the intersection between the curved surface and the blue plane is drawn in blue.