Class 12 Vector Algebra · Long Answer3 Marksorthogonality
Class 12 Maths · Vector Algebra · Long Answer #112
Find a unit vector perpendicular to a+b and a−b, where a=(1,1,1), b=(1,2,3).
✅ Step-by-Step Solution
Final Answer: ±(−1,2,−1)/√6
- Compute a+b=(2,3,4), a−b=(0,−1,−2).
- Their cross product is (−2,4,−2)=2(−1,2,−1).
- Its norm is 2√6.
- The unit normals are ±(−1,2,−1)/√6.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Compute a+b=(2,3,4), a−b=(0,−1,−2).
- [1 mark] Their cross product is (−2,4,−2)=2(−1,2,−1).
- [1 mark] Its norm is 2√6.
- [0.5 marks] The unit normals are ±(−1,2,−1)/√6.
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