NCERT Class 12 · Ch 10 Miscellaneous Exercise · Q15
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Miscellaneous Exercise Question 15
For nonzero a,b prove (a+b)·(a+b)=|a|²+|b|² iff a,b are perpendicular.
💡 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 equality is equivalent to a·b=0.
- Expand the left side: |a|²+2a·b+|b|².
- The stated equality holds exactly when 2a·b=0. For nonzero Euclidean vectors this is exactly perpendicularity; both directions follow.
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