Math20C_Formulae1

Math20C_Formulae1 - UCSD 2005–2006 Spring Math 20C –...

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Unformatted text preview: UCSD 2005–2006 Spring Math 20C – Calculus & Analytic Geometry For Science & Engineering Formulae for the first mid-term examination • For a = a1 i + a2 j + a3 k and b = b1 i + b2 j + b3 k, a×b= a2 a3 aa aa i+ 3 1 j+ 1 2 k= b2 b3 b3 b1 b1 b2 ijk a1 a2 a3 b1 b2 b3 = (a2 b3 − a3 b2 )i + (a3 b1 − a1 b3 )j + (a1 b2 − a2 b1 )k. • For a = a1 i + a2 j + a3 k, b = b1 i + b2 j + b3 k, and c = c1 i + c2 j + c3 k, a · (b × c) = a1 a2 a3 b1 b2 b3 c1 c2 c3 = a1 b2 c3 + a2 b3 c1 + a3 b1 c2 − a3 b2 c1 − a2 b1 c3 − a1 b3 c2 1 ...
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