Class 12 Vector Algebra · Long Answer3 Marksvector_equations
Class 12 Maths · Vector Algebra · Long Answer #71
Let a=(1,4,2), b=(3,−2,7), c=(2,−1,4). Find p perpendicular to a,b with p·c=18.
✅ Step-by-Step Solution
Final Answer: p=(64,−2,−28)
- Compute a×b=(32,−1,−14), which is nonzero.
- Every common perpendicular is p=t(32,−1,−14).
- Its dot product with c is t(64+1−56)=9t. Set 9t=18, giving t=2.
- Thus p=(64,−2,−28); its dot products with a,b vanish and with c equal 18.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Compute a×b=(32,−1,−14), which is nonzero.
- [1 mark] Every common perpendicular is p=t(32,−1,−14).
- [1 mark] Its dot product with c is t(64+1−56)=9t. Set 9t=18, giving t=2.
- [0.5 marks] Thus p=(64,−2,−28); its dot products with a,b vanish and with c equal 18.
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