Class 12 Vector Algebra · Short Answer2 Marksorthogonality
Class 12 Maths · Vector Algebra · Short Answer #57
For a = (1,2,−3), b = (3,−1,2), show a + b is perpendicular to a − b.
✅ Step-by-Step Solution
Final Answer: (a + b) ⟂ (a − b).
- Compute a + b = (4,1,−1) and a − b = (−2,3,−5).
- Their dot product is −8 + 3 + 5 = 0.
- Both are nonzero, so a + b and a − b are perpendicular.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Compute a + b = (4,1,−1) and a − b = (−2,3,−5).
- [1 mark] Their dot product is −8 + 3 + 5 = 0.
- [0.5 marks] Both are nonzero, so a + b and a − b are perpendicular.
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