Class 12 Vector Algebra · Long Answer3 Marksvector_identities
Class 12 Maths · Vector Algebra · Long Answer #121
For a=(1,2,1), b=(3,2,−7), c=(5,6,−5), verify a×(b×c)=(a·c)b−(a·b)c.
✅ Step-by-Step Solution
Final Answer: Both sides equal (36,24,−84).
- Compute b×c=(32,−20,8).
- Then a×(b×c)=(36,24,−84).
- Also a·c=12 and a·b=0. Thus (a·c)b−(a·b)c=12(3,2,−7)=(36,24,−84).
- Both sides equal (36,24,−84), verifying the identity.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Compute b×c=(32,−20,8).
- [1 mark] Then a×(b×c)=(36,24,−84).
- [1 mark] Also a·c=12 and a·b=0. Thus (a·c)b−(a·b)c=12(3,2,−7)=(36,24,−84).
- [0.5 marks] Both sides equal (36,24,−84), verifying the identity.
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