NCERT Class 12 · Ch 10 Miscellaneous Exercise · Q11
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Miscellaneous Exercise Question 11
Show the direction cosines of a nonzero vector equally inclined to OX,OY,OZ are ±(1/√3,1/√3,1/√3).
💡 Concept Hints
- Write the vector components and identify the required direction or geometric relation.
- Use the magnitude, dot-product, cross-product or section formula that matches the requested quantity.
✅ Step-by-Step Solution
Final Answer: The two triples are (1,1,1)/√3 and (−1,−1,−1)/√3.
- Equal angles to the positive axes give l=m=n.
- Since l²+m²+n²=1, 3l²=1 and l=±1/√3. The signs agree across the three components.
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