TEAM PROJECT. Useful Fonnulas for Two and More Vectors.
Chapter 9, Problem 9.3(choose chapter or problem)
TEAM PROJECT. Useful Fonnulas for Two and More Vectors. Prove (12)-06). which are often useful in practical work. and illustrate each formula with two examples. Hillts. For (13) choose Cartesian coordinates such that d = [c11, 0, 0] and c = [Cl, C2. 0]. Show thatach side of (13) then equals [-b2C2dl' b1C2dl' 0]. andgive reasons why the two sides are then equal in anyCartesian coordinate system. For (14) and (15) use (13).Formula (15) is called Lagrange's identity. (12) la x bl = Y(aoa)(bob) - (a ob)2(13) b x (c x d) = (bod)c - (boc)d(14) (a x b) x (c x d)= (a b d)c - (a b c)d(15) (a x b)o(c x d) = (aoc)(bod) - (aod)(boc)(a b c) = (b c a) = (c a b)(16) = -(c b a) = -(a c b)
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