a. Parameterize by
with .
b/c. The line integral of over is
d. Notice that we can write the line integral as
By Green's theorem, the line integral is equivalent to
where is the triangle bounded by , and this integral is simply twice the area of . is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.
I don't know this. Sorry. Good luck
The value of X is 35 because the angle 35 measures the same as the angle X, hence their values are the same
The <em>xy</em>-plane has a normal vector of 〈0, 0, 1〉, and any plane parallel to it will have the same normal vector.
Then the equation of the plane through (6, 3, 2) that is parallel to the <em>xy</em>-plane has equation
〈<em>x</em> - 6, <em>y</em> - 3, <em>z</em> - 2〉 • 〈0, 0, 1〉 = 0
==> <em>z</em> - 2 = 0
==> <em>z</em> = 2