Class 12 Vector Algebra · Long Answer3 Marksvector_projection
Class 12 Maths · Vector Algebra · Long Answer #76
For a=(2,−1,−2), b=(7,2,−3), express b=b₁+b₂ with b₁ parallel to a and b₂ perpendicular to a.
✅ Step-by-Step Solution
Final Answer: b₁=(4,−2,−4), b₂=(3,4,1)
- Use b₁=[(b·a)/(a·a)]a.
- Compute b·a=14−2+6=18 and a·a=9; hence b₁=2a=(4,−2,−4).
- Then b₂=b−b₁=(3,4,1), and b₂·a=6−4−2=0.
- Thus b=(4,−2,−4)+(3,4,1), with the required parallel and perpendicular components.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Use b₁=[(b·a)/(a·a)]a.
- [1 mark] Compute b·a=14−2+6=18 and a·a=9; hence b₁=2a=(4,−2,−4).
- [1 mark] Then b₂=b−b₁=(3,4,1), and b₂·a=6−4−2=0.
- [0.5 marks] Thus b=(4,−2,−4)+(3,4,1), with the required parallel and perpendicular components.
Master Chapter 10: Vector Algebra
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Vector Algebra.
← Previous Question
Find the area of parallelogram ABCD with AB=(3,1,4), AC=(4,0,5).
Next Question →Vectors a=(p,q,r), b=(s,3,4), c=(3,1,−2) satisfy a=b+c and form a…
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…