Class 12 Vector Algebra · Long Answer3 Marksvector_equations
Class 12 Maths · Vector Algebra · Long Answer #114
Let a=(1,4,2), b=(3,−2,7), c=(2,−1,4). Find d perpendicular to a,b with c·d=27.
✅ Step-by-Step Solution
Final Answer: d=(96,−3,−42)
- Compute a×b=(32,−1,−14)≠0.
- Write d=t(32,−1,−14).
- Then c·d=t(64+1−56)=9t=27, so t=3.
- Therefore d=(96,−3,−42); substitution verifies all three dot conditions.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Compute a×b=(32,−1,−14)≠0.
- [1 mark] Write d=t(32,−1,−14).
- [1 mark] Then c·d=t(64+1−56)=9t=27, so t=3.
- [0.5 marks] Therefore d=(96,−3,−42); substitution verifies all three dot conditions.
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