Question

I don't need all the cross products to be solved for me, just a couple so I can see how its done! (preferably the ixj=k and the ixk=-j

Figure 3.17 displays the unit vectors i, j, and k along the ac, y, and z axes. The positive directions for these axes, and the directions for the unit vectors, have been chosen according to the standard convention for a "right-handed” coordinate system (if, say, the positive direction of the x axis and the direction of i were reversed, the coordinate system would become "left-handed"). Use the right-hand rule to establish the following multiplication table for the unit vectors displayed in Fig. 3.17 [see Eqs.(3.31) and (3.32)]: ixi=0 jxi=-k kxi-j ixj=k jxj=0 kxj=i ixk= j jxk= i . kxk=0

Answer 1

The cross product is defined as - Å x B = lAllBl sino ñ where, o be the angle between Å and B in the unit vector perpendicular to both son ix} = (illjl Sin 90 ĥ and in Å and B. 1. Here ĥ is vecter herfrendicular to î &Î is į and bey right hand palm rule, the direction is also along + Zaxis ,Do S ix i = ŕ Similarly, ix R = lill Ål sin 90 ñ By right hand halm rule, the duection is along Live yaxis , so î xŘ= -ĵ