Class 12 Vector Algebra · Long Answer3 Marksorthogonality
Class 12 Maths · Vector Algebra · Long Answer #74
Find a unit vector normal to the plane through A=(3,−1,2), B=(1,−1,−3), C=(4,−3,1).
✅ Step-by-Step Solution
Final Answer: ±(−10,−7,4)/√165
- Compute AB=(−2,0,−5) and AC=(1,−2,−1).
- Their cross product is (−10,−7,4).
- Its norm is √(100+49+16)=√165.
- The two unit normals are ±(−10,−7,4)/√165; either is a valid answer.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Compute AB=(−2,0,−5) and AC=(1,−2,−1).
- [1 mark] Their cross product is (−10,−7,4).
- [1 mark] Its norm is √(100+49+16)=√165.
- [0.5 marks] The two unit normals are ±(−10,−7,4)/√165; either is a valid answer.
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