Problems and solutions I

We will specify the direction with a unit vector u

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Unformatted text preview: or. ` The magnitude of this vector is A B sin q. We will specify the direction with a unit vector u. The two vectors A and B define a plane; their cross product is perpendicular to that plane. There are two unit vectors perpendicular to any plane; we use the right hand rule to find the correct one. Put your right thumb in the direction of the first entry A and your fingers in the direction of the second entry B. The palm of your hand is in the ` direction u, giving the direction of the cross product. `` A ä B = A B sin q u Iu by right hand ruleM Into Out of Figure: The convention we use to represent the third dimension relative to some two dimensional figure is to use a dot to represent "out of" and an × to represent "into". A useful way to remember this is with an arrow; if it points at you it is a dot and away an ×. Properties of the Cross Product A ä B = -B ä A Hantisymmetry - not commutativeL IA ä BM ä C ¹Ȧ A ä IB ä CM Hnot associativeL Ic AM ä B = c IA ä BM = A ä Ic BM Hassociative w.r.t. scalar mult.L IA + BM ä C = A ä C + B ä C and A ä IB + CM = A ä B + A ä C HdistributiveL The Cross Product and Components With the dot product we were able to write it in terms of components. We can do the same for the cross product. As before we ha...
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