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

Find × F if F=y2z, i+xz2, j+x2y, k.

1. ≤ft(x2 - 2 x z ), i - ≤ft(2 x y - y2 ), j - ≤ft(2 y z - z2 ), k
2. -≤ft(x2 - 2 x z ), i + ≤ft(2 x y - y2 ), j + ≤ft(2 y z - z2 ), k
3. ≤ft(x2 + 2 x z ), i + ≤ft(2 x y + y2 ), j + ≤ft(2 y z + z2 ), k
4. -≤ft(2 x y - y2 ), i - ≤ft(2 y z - z2 ), j + ≤ft(x2 - 2 x z ), k

Answer

A. ≤ft(x2 - 2 x z ), i - ≤ft(2 x y - y2 ), j - ≤ft(2 y z - z2 ), k

Solution

× F=≤ft( F3/ y- F2/ z ) i+≤ft( F1/ z- F3/ x ) j+≤ft( F2/ x- F1/ y ) k=(x2-2xz) i+(y2-2xy) j+(z2-2yz) k.

More Vector Calculus: Gradient, Divergence, and Curl questions

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

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