The line integral of the vector field,along the boundary of thetriangle with vertices(1,0,0), (0,2,0), and (0,0,1), oriented anticlock wise, whenviewed from the point (2,4,2) isa)1/6b)7/6c)0d)1/2Correct answer is option 'B'. Can you explain this answer?

Question

Answer

we will compute

Let S is the surface of Δ ABC, then the eqnof surface is given by

Now here to evaluate (1), we can use stokes theorem Then we have

where

is outward going UNV to S and given by

Now

= i(z) - j (-x) + k(y) = zi + xj + yk

Now take orthogonal projection of S on the xy-plane.

then we have

Then by (2)

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