Class 12 Vector Algebra · Long Answer3 Marksvector_equations
Class 12 Maths · Vector Algebra · Long Answer #69
For a=(1,1,1), b=(0,1,−1), find c such that a×c=b and a·c=3.
✅ Step-by-Step Solution
Final Answer: c=(5/3,2/3,2/3)
- Put c=(x,y,z). Then a×c=(z−y,x−z,y−x).
- Compare with (0,1,−1): z=y and x=z+1. The dot condition gives x+y+z=3.
- Substitute x=y+1, z=y to get 3y+1=3; hence y=z=2/3 and x=5/3.
- Therefore c=(5/3,2/3,2/3); substitution verifies both prescribed products.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Put c=(x,y,z). Then a×c=(z−y,x−z,y−x).
- [1 mark] Compare with (0,1,−1): z=y and x=z+1. The dot condition gives x+y+z=3.
- [1 mark] Substitute x=y+1, z=y to get 3y+1=3; hence y=z=2/3 and x=5/3.
- [0.5 marks] Therefore c=(5/3,2/3,2/3); substitution verifies both prescribed products.
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