GATE AE 2022 • Q24 MSQ • 1 Mark Aerospace Structures

Aerospace Structures

Strength of Materials & Elasticity

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Question Statement:

If $\hat{a}, \hat{b}, \hat{c}$ are three mutually perpendicular unit vectors, then $\hat{a} \cdot (\hat{b} \times \hat{c})$ can take the value(s):

Options:

  • (A) 0
  • (B) 1
  • (C) -1
  • (D) $\infty$

Official Answer Key:

B, C

Step-by-Step Solution & Explanation

### **Detailed Step-by-Step Solution (GATE AE 2022 Q.24)** **1. Scalar Triple Product of Orthonormal Vectors**: For mutually perpendicular unit vectors, $\hat{b} \times \hat{c} = \pm \hat{a}$. Hence: $$\hat{a} \cdot (\hat{b} \times \hat{c}) = \hat{a} \cdot (\pm \hat{a}) = \pm 1$$ It is $+1$ for a right-handed system and $-1$ for a left-handed system. - **Official Answer Key**: **B, C**
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