Engineering Board Exam Reviewer · Vector Calculus: Gradient, Divergence, and Curl · easy

Find if =x2y+z.

1. x2, i + 2 x y, j + k
2. 2 x y, i + x2, j + z, k
3. 2 x y, i + x2, j + k
4. 2 x y, i + x2, j

Answer

C. 2 x y, i + x2, j + k

Solution

= / x i+ / y j+ / z k=2xy, i+x2 j+ k.

More Vector Calculus: Gradient, Divergence, and Curl questions

1. Evaluate C(x,dy-y,dx) counterclockwise around the circle x2+y2=4.
2. The field F=(2xy+z3), i+x2, j+3xz2, k is conservative. Find a scalar potential with F= .
3. Find the directional derivative of =x2+yz at (1,2,1) in the direction of i+2 j+2 k.
4. Find × F if F=y2z, i+xz2, j+x2y, k.
5. Find · F if F=x2y, i+yz2, j+xz, k.

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