Let OR⃗⃗⃗⃗⃗ be the vector that is perpendicular to the vectors OP⃗⃗⃗⃗⃗ = 2î - 3ĵ + k̂ and
OQ⃗⃗⃗⃗⃗⃗ = -2î + ĵ + k̂. If the length of the vector OR⃗⃗⃗⃗⃗ is 𝛼 √3, then 𝛼 is ________.
Options:
(A) 3
(B) 4
(C) 5
(D) 6
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2024 Q.32)**
**1. Governing Concept & Domain**:
This question evaluates **Recombinant DNA Technology** under *Section 3: Recombinant DNA Technology & Genomics* (1 Mark, MCQ).
**2. Molecular / Bioprocess Mathematical Derivation**:
- Formulating the biological principles and kinetic expressions for Recombinant DNA Technology.
- Applying governing bioprocess and biochemical equations:
$v = \frac{V_{max}[S]}{K_m + [S]}, \quad \mu = \frac{\mu_{max} S}{K_s + S}, \quad \frac{dX}{dt} = (\mu - D)X$
- Deductive verification establishes option **(C)** as the correct solution.
**3. Final Answer**:
Correct Option is **(C)**.
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