sln1 - HW#1 Problem 1 Bound vectors (position vector) have...

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HW#1 Problem 1 Bound vectors (position vector) have a specific origin and a point of application, whereas free vectors (a couple) do not. Problem 2 Several proofs exist for these. (i) Schwartz Inequality cos uv θ •≤ The two sides will be equal only when cos 1 = . (ii) Triangular Inequality 2 22 2 () 2 c o s ()2 u v uv uv u u v v L H S u v u uv v RHS +≤ + +=+ •+=+ + += ++ The two sides will be equal only when cos 1 = . Problem 3 2 2 0 () ( 0 aa aa a dd a dt dt a a •• •= ) 0 a = b/c derivative of scalar. The expression 0 is always true b/c vector a is of the fixed length. Problem 4 ˆ ˆˆ r rr rk r dr d e dt dt re r e r e e r e ω == =+× =+ × ˆ r
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2 2 ˆˆ () ( ) ˆ ˆ ˆ ˆˆˆ ˆ ( ˆˆˆˆ ˆ ˆ r r rr rk r k r dr d e r e dt dt dd re r e dt dt r e r e re re r e r e e r e r e r e e r e re re re r e e θ θθ ˆ ) ωθ ω θθθ •• •• •• • • •• •• • • •• •• • • • • •• •• == + =+ =+×+ + + × ×+ + + × =+ + + − =− + ˆ (2 ) e •• • • + Problem 5 d VR R R dt = + D R × R D - relative, R × - tangential ( ) ( ) 2( AV RR dt dt dt dt ) R ωω + × =+× =+×+ ×+× × D D DD D D R R DD
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sln1 - HW#1 Problem 1 Bound vectors (position vector) have...

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