MATH 127
Vector Analysis
♦ Books: (1) Vector Analysis - Sam Series
(2) Linear Algebra - Abdur Rahman
scalar → Magnitude
Vector → Magnitude + Direction
→A=a1ˆi+a2ˆj+a3ˆk
|→A=√a12+a22+a33→Magnitude of →A
ˆi,ˆj,ˆk →Standard basic vector → Unit Vector• Unit Vector → Magnetitude = 1
Proof:
ˆa=→A|→A|=a1√a12+a22+a32ˆi+a2√a12+a22+a32ˆj+a3√a12+a22+a32ˆk|ˆa|=√(a1√a12+a22+a32 ˆi)2+(a2√a12+a22+a32 ˆj)2+(a3√a12+a22+a32 ˆk)2√a12+a22+a32a12+a22+a32=1
→A=a1ˆi+a2ˆj+a3ˆk=(a1,a2,a3) →Components
→A=→B⟹ |→A|=|→B| and same direction→A=−→B⟹ |→A|=|→B| but has opposite direction
• Position Vector:
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