1. Use Stokes’ Theorem to evaluate ∬ curF⃗ ∙ dS⃗ S where F⃗ = x 3 i⃗ + (4y − z 3y 3 )j⃗ + 2xk⃗⃗ and S is the portion of z = x 2 + y 2 − 3 below z = 1 with orientation in the negative z-axis direction. 2. Use Stokes’ Theorem to evaluate ∬ curF⃗ ∙ dS⃗ S where F⃗ = 2yi⃗ + 3xj⃗ + (z − x)k⃗⃗ and S is the portion of y = 11 − 3x 2 − 3z 2 in front of y = 5 with orientation in the positive y-axis direction. 3. Use Stokes’ Theorem to evaluate ∫ F⃗ ∙ dr⃗ C where F⃗ = (zx 3 − 3z)i⃗ + xzj⃗ + yxk⃗⃗ and C is the triangle with vertices (0,0,4), (0,2,0), and (2,0,0). C has the orientation seen in the sketch below.

< 4, -5>

step-by-step explanation:

starting from g. we move 4 right and then 5 down to get to h. that means the vector is < 4, -5>

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column

just get this app called photo math it should be able to do those