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GATE 2020 ME (ME2) – Question 36

Engineering Mathematics · Calculus: Gradient, divergence, curl, vector identities, line, surface and volume integrals · 2 marks · Multiple choice

Find the directional derivative of $f(x,y,z)=xyz$ at (−1,1,3) in the direction $\hat i-2\hat j+2\hat k$.

  1. $3\hat i-3\hat j-\hat k$
  2. $-7/3$
  3. $7/3$
  4. 7

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Correct answer: (C) $7/3$

Explanation

Gradient is (yz,xz,xy)=(3,−3,−1). Direction length is√(1+4+4)=3, so unit vector is(1,−2,2)/3. Dot product is(3+6−2)/3=**7/3,C**. The gradient vector itself is not the scalar directional derivative.