Class 12 Vector Algebra · Long Answer3 Marksvector_equations
Class 12 Maths · Vector Algebra · Long Answer #117
For a=(2,1,−1), b=(4,−7,1), find c with a×c=b and a·c=6.
✅ Step-by-Step Solution
Final Answer: c=(3,2,2)
- Put c=(x,y,z). Then a×c=(z+y,−x−2z,2y−x).
- Equate to b: y+z=4, x+2z=7, 2y−x=1. Also 2x+y−z=6.
- Use y=4−z and x=7−2z in the dot condition: 18−6z=6, giving z=2, y=2, x=3.
- Therefore c=(3,2,2), satisfying both conditions.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Put c=(x,y,z). Then a×c=(z+y,−x−2z,2y−x).
- [1 mark] Equate to b: y+z=4, x+2z=7, 2y−x=1. Also 2x+y−z=6.
- [1 mark] Use y=4−z and x=7−2z in the dot condition: 18−6z=6, giving z=2, y=2, x=3.
- [0.5 marks] Therefore c=(3,2,2), satisfying both conditions.
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