NCERT Class 12 · Ch 10 Miscellaneous Exercise · Q4
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Miscellaneous Exercise Question 4
If a=b+c, must |a|=|b|+|c|? Justify.
💡 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: No; equality requires b,c to have the same direction, apart from zero cases.
- Take b=i,c=j. Then a=i+j has magnitude √2 while |b|+|c|=2.
- In general the triangle inequality gives |b+c|≤|b|+|c|; equality requires the same-direction condition.
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