Problems and solutions I

# It follows then that 0 x x y y z z chapter

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Unformatted text preview: ve to find the products of the basis unit vectors. Because of the antisymmetry property we get A ä A = 0. It follows then that `` `` `` 0 = x ä x = y ä y = z ä z. Chapter I - Rotational Dynamics and Equilibrium | 3 Using our definition of the cross product we can see that the cross product of two perpendicular unit vectors is a third unit vector perpendicular to the two. ` `` ` A ä B = A B sin q u ï v ä w = 1 ÿ 1 ÿ 1 u ` ` ` ` The cross product of the unit vectors x and y is thus a unit vector perpendicular to the xy plane. This is either z or -z. We insist that our coordinate system is right-handed; this means that `` ` x ä y = z. For the other combinations of unit vectors there is a simple rule to keep track of their cross products. Arrange x, y and z around a circle. x z y If the order of the three coordinates has the same sense of rotation as x, y, z it gains a positive sign. If opposite it gets a minus sign. `` ` `` ` y ä z = x, z ä x = y , `` ` `` ` `` ` y ä x = -z, x ä z = -y and z ä y = -x We can put all this together and get the cross product in terms of components. ` ` ` ` ` ` A ä B = I A x x + A y y + A z zM ä I B x x + B y y + B z zM ` ` ` = x I A y Bz - Az B y M + y H Az B x - A x Bz L + z I A x B y - A y B x M The determinant method is a common way to write this....
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## This document was uploaded on 02/26/2014 for the course PHYS 2425 at Blinn College.

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