Vector..................?

we can calculate the component of a vector A in the direction of a vector B by taking the dot product of the unit vector in the B direction (b=B/|B|) with A. ie b dot A. Show that you can find the component of A perpendicular to the vector B by taking the product:-bx(bxA). you will need to write A as A1+A2(with respect to b) and use the BAC-CAB rule.|||Using the suggestion


A = A1 + A2 where A1 is the component in the direction of B, and A2 is the component perpendicular to B.


Now bxA1 = 0,


hence


bxA


=bxA1 + bxA2


= bxA2





That's a start, and I guess you finish it by taking the cross product


-bx(bxA) = -bx(bxA2)





and I would have known how to proceed from there, but don't remember now. Maybe you can show the righthand side is equal to A2. Or try a website such as Wolfram.





Is there a formula for triple cross product something like





ux(vxw) = (u.w)v - (u.v)w?





If so, in this case the first term is (-b.A2)b which is zero since A2 is perpendicular to b, and the second is


(b.b)A2, which is A2 since b.b = 1 for any unit vector.