NCERT Class 12 · Ch 10 Exercise 10.3 · Q11
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Exercise 10.3 Question 11
Show |a|b+|b|a is perpendicular to |a|b−|b|a for nonzero a,b.
💡 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: Their dot product is zero.
- Let u=|a|b and v=|b|a. Then (u+v)·(u−v)=|u|²−|v|².
- Both squared lengths equal |a|²|b|², so their difference is zero. For collinear a,b one of the constructed vectors may be zero; the algebraic dot-zero statement remains valid, but an angle to the zero vector is undefined.
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