Class 12 Vector Algebra · Long Answer3 Marksunit_vectors
Class 12 Maths · Vector Algebra · Long Answer #118
Adjacent sides of a parallelogram are a=(1,2,3), b=(2,4,−5). Find unit vectors parallel to its diagonals.
✅ Step-by-Step Solution
Final Answer: ±(3,6,−2)/7 and ±(1,2,−8)/√69
- The diagonal vectors are d₁=a+b=(3,6,−2), d₂=b−a=(1,2,−8).
- Compute |d₁|=√(9+36+4)=7.
- Compute |d₂|=√(1+4+64)=√69.
- Thus unit vectors parallel to the diagonals are ±(3,6,−2)/7 and ±(1,2,−8)/√69.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The diagonal vectors are d₁=a+b=(3,6,−2), d₂=b−a=(1,2,−8).
- [1 mark] Compute |d₁|=√(9+36+4)=7.
- [1 mark] Compute |d₂|=√(1+4+64)=√69.
- [0.5 marks] Thus unit vectors parallel to the diagonals are ±(3,6,−2)/7 and ±(1,2,−8)/√69.
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