The direction in which a scalar field
( , , )x y z has the largest rate of change at
any point with position vector
ˆˆˆr xi yj zk= + +
is the same as that of the vector
Options:
(A)
(B) () r
(C) r
(D) (𝛻𝜙 • dr⃗)r⃗
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2023 Q.11)**
**1. Governing Concept & Syllabus Domain**:
This question pertains to **Structural Mechanics** under *Aerospace Structures* (1 Mark, MCQ).
**2. Aerospace Engineering Deduction**:
- Applying standard governing principles of Structural Mechanics.
- Option **(A)** matches the analytical derivation and official criteria.
**3. Final Answer**:
Correct Option is **(A)**.
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