This simplifies to $\frac{1}{a^2} + \frac{1}{a^2} + \frac{1}{a^2} = 1$, which further simplifies to $\frac{3}{a^2} = 1$.
Multiplying both sides by $a^2$ gives $3 = a^2$.
Taking the square root of both sides gives $a = \pm\sqrt{3}$.
Correct Answer: $a=\pm\sqrt{3}$
AI Suggestion: Option D
AI generated content. Review strictly for academic accuracy.
Pedagogical Audit
Bloom's Analysis:
This is an APPLY question because the student needs to apply the concept of direction cosines and their relationship to solve for the value of 'a'.
Knowledge Dimension:CONCEPTUAL
Justification:The question requires understanding the conceptual relationship between direction cosines and their property that the sum of their squares equals 1.
Syllabus Audit:
In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding of a specific concept (direction cosines) from the textbook.