Class 12 Vector Algebra · Short Answer2 Marksvector_identities
Class 12 Maths · Vector Algebra · Short Answer #110
Find |a| and |b| if |a|=2|b| and (a+b)·(a−b)=12.
✅ Step-by-Step Solution
Final Answer: |a|=4, |b|=2
- The dot product equals |a|²−|b|².
- Put |b|=r≥0; then 4r²−r²=12, giving r²=4 and r=2.
- Thus |b|=2 and |a|=4.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The dot product equals |a|²−|b|².
- [1 mark] Put |b|=r≥0; then 4r²−r²=12, giving r²=4 and r=2.
- [0.5 marks] Thus |b|=2 and |a|=4.
Master Chapter 10: Vector Algebra
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Vector Algebra.
← Previous Question
Unit vectors a,b have √3a−b also unit. Find their angle.
Next Question →Find a unit vector perpendicular to (4,3,1) and (2,−1,2).
More Practice Questions in Vector Algebra
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…