(c) Calculate the divergence (V.Ä = div Ã) and curl (V × Ā = rot Á). of the following vector fields. (i) Ã(x,y, z) = xē, + yēy + zē; (ii) Ã(x, y, z) = x²ē, + y?ē, + z²ē, en + Ey + ēz Vx² + y² + z² ex + ey (iii) Ã(x, y, 2) = + ēz x² + y? + z2 -yēr + xẽy x² + y? (iv) Ã(x, y, z) = (v) Ã(x, y, z) = (vi) A(p, Ф, г) — —ёр (vii) Ã(r, 0, ø) (viii) Ã(r, 0, ø)

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Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.