NCERT Class 12 · Ch 10 Exercise 10.4 · Q4
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Exercise 10.4 Question 4
Prove (a−b)×(a+b)=2(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: The identity holds.
- Distribute: a×a+a×b−b×a−b×b.
- Self-cross products vanish, and b×a=−a×b. The remaining sum is 2(a×b).
Master Chapter 10: Vector Algebra
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Vector Algebra.
← Previous Question
A unit vector makes angles π/3 with i, π/4 with j and acute θ with…
Next Question →Find λ,μ if (2i+6j+27k)×(i+λj+μk)=0.
Related Questions in Vector Algebra
Class 12 Vector Algebra · Mcq Single Correct
Find |a × b|² + (a · b)².
Class 12 Vector Algebra · Mcq Single Correct
Find the area of triangle OAB, where OA = (1,2,3) and OB = (−3,−2,1).
Class 12 Vector Algebra · Mcq Single Correct
For nonzero vectors a,b with angle θ ∈ [0,π], when is a · b ≥ 0?
Class 12 Vector Algebra · Mcq Single Correct
For a vector a, find (a · i)i + (a · j)j + (a · k)k.
Class 12 Vector Algebra · Mcq Single Correct
Which vector has magnitude 9 and the same direction as (1,−2,2)?
Class 12 Vector Algebra · Mcq Single Correct
Find the position vector dividing the segment from 2a − 3b to a + b internally in the ratio…