Explanation Given: Area of region R = 1 2 ‖ N ‖ 2 ∮ C ( b z − c y ) d x + ( c x − a z ) d y + ( a y − b x ) d z Calculation: Let us first find the equation of the plane containing the vertices. Equation of plane will be: x + y + z = 1 A vector normal to the plane will be N = 〈 1 , 1 , 1 〉 ⇒ ‖ N ‖ = 1 2 + 1 2 + 1 2 = 3 . We can now set up the area for the triangle with known vertices as: ⇒ Area of region R = 1 2 ‖ N ‖ 2 ∮ C ( b z − c y ) d x + ( c x − a z ) d y + ( a y − b x ) d z ⇒ Area of region R = 1 2 ( 3 ) 2

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Author: Rogawski

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Chapter 18, Problem 40CRE

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Area of the triangle with vertices $(1, 0, 0), (0, 1, 0), (0, 0, 1)$ using line integral.

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Chapter 18, Problem 39CRE

Chapter 18, Problem 41CRE

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Chapter 18 Solutions

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To prove: Area of the triangle with vertices ( 1 , 0 , 0 ) , ( 0 , 1 , 0 ) , ( 0 , 0 , 1 ) using line integral.

Solution Summary: The equation of the plane containing the vertices will be: x + y + 1. We can now set up the area for the triangle with known

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To prove:

Area of the triangle with vertices $(1, 0, 0), (0, 1, 0), (0, 0, 1)$ using line integral.

Want to see the full answer?

Chapter 18 Solutions

To prove: Area of the triangle with vertices ( 1 , 0 , 0 ) , ( 0 , 1 , 0 ) , ( 0 , 0 , 1 ) using line integral.

Solution Summary: The equation of the plane containing the vertices will be: x + y + 1. We can now set up the area for the triangle with known

Videos

To prove: Area of the triangle with vertices (1,0,0),(0,1,0),(0,0,1) using line integral.

Want to see the full answer?

Chapter 18 Solutions

To prove:

Area of the triangle with vertices $(1, 0, 0), (0, 1, 0), (0, 0, 1)$ using line integral.