Class 12 Vector Algebra · Long Answer3 Marksorthogonality
Class 12 Maths · Vector Algebra · Long Answer #116
For a=(2,−1,3), b=(3,1,−2), find the angle between a+b and a−b and a nonzero vector perpendicular to both.
✅ Step-by-Step Solution
Final Answer: Angle π/2; one perpendicular is (2,−26,−10)
- Compute s=a+b=(5,0,1), t=a−b=(−1,−2,5).
- Their dot product is −5+0+5=0 and both are nonzero, so their angle is π/2.
- Compute s×t=(2,−26,−10).
- Thus the angle is π/2 and (2,−26,−10) is one valid common perpendicular.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Compute s=a+b=(5,0,1), t=a−b=(−1,−2,5).
- [1 mark] Their dot product is −5+0+5=0 and both are nonzero, so their angle is π/2.
- [1 mark] Compute s×t=(2,−26,−10).
- [0.5 marks] Thus the angle is π/2 and (2,−26,−10) is one valid common perpendicular.
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