Project ForgeEngineering Mathematics
Calculus
GATE 2020
Medium
The directional derivative of f(x,y,z) = xyz at point (−1,1,3) in the direction of vector î − 2ĵ + 2k̂ is
- A3î − 3ĵ − k̂
- B−7/3
- 7/3
- D7
Explanation
∇f = (yz, xz, xy). At (−1,1,3): ∇f = (1×3, −1×3, −1×1) = (3,−3,−1). Unit vector of (1,−2,2): magnitude=√(1+4+4)=3, so û=(1/3,−2/3,2/3). Directional derivative = ∇f·û = 3(1/3) + (−3)(−2/3) + (−1)(2/3) = 1+2−2/3 = 7/3.
Source: GATE ME 2020 Session 2 (ME-2) (2020)
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