Find the Point(s) on the Surface $x ^ { 2 } + y ^ { 2 } - z ^ { 2 } = 1$

question 74

Essay

Find the point(s) on the surface $x ^ { 2 } + y ^ { 2 } - z ^ { 2 } = 1$ such that the normal vector at the point is parallel to the vector $\{ 1,1 , - 1 \}$ .

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Definitions:

Stone's Footnote 4

A famous footnote in United States constitutional law, highlighting circumstances under which courts may have an enhanced duty to scrutinize legislation.

Carolene Products Co.

A landmark U.S. Supreme Court case notable for its Footnote Four, which suggested that certain cases, particularly those involving civil rights and liberties, should be given more exacting judicial scrutiny.

Brandenburg v. Ohio

A 1969 Supreme Court decision that established the government cannot punish inflammatory speech unless that speech is likely to incite imminent lawless action.

Supreme Court

The highest federal court in the United States, with ultimate appellate jurisdiction over all federal and state court cases involving issues of federal law.