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NCERT Class 12 · Ch 10 Miscellaneous Exercise · Q14

NCERT Class 12 Maths · Chapter 10 Vector Algebra · Miscellaneous Exercise Question 14

If a,b,c are mutually perpendicular nonzero vectors of equal magnitudes, show that a+b+c is equally inclined to a,b,c.

💡 Concept Hints

  1. Write the vector components and identify the required direction or geometric relation.
  2. Use the magnitude, dot-product, cross-product or section formula that matches the requested quantity.

✅ Step-by-Step Solution

Final Answer: Each angle is cos⁻¹(1/√3).
  1. Let s=a+b+c and let each magnitude be r>0. Orthogonality gives |s|²=3r², hence |s|=√3r.
  2. The dot products s·a=s·b=s·c=r².
  3. Each angle therefore has cosine r²/(√3r·r)=1/√3, proving equal inclination.

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