By applying Stokes theorem, the value of where C is the boundary of the triangle with vertices (2, 0, 0), (0, 3, 0) and (0, 0, 6), is

Question

Question

This question was previously asked in

BPSC Asstt. Prof. ME Held on Nov 2015 (Advt. 22/2014)

Answer 1

Concept:

By stokes theorem:

Calculation:

Given:

Equation of the plane through A, B, C is

∴ ϕ = 3x + 2y + z - 6 represents equation of the surface.

Vector normal to the surface is given by gradient:

Unit vector n̂:

A (2, 0, 0), B (0, 3, 0) and C (0, 0, 6)

⇒ [(0 - 2), (3 - 0), (0 - 0)] = (-2, 3, 0)

⇒ [(0 - 0), (0 - 3), (6 - 0)] = (0, -3, 6)