Question with vectors and cross products...?

Ok, This question is three parts, and I got the first, but...





At time t, the vector from the origin to a moving point is r = a cos (wt) + b sin (wt), where a, b, and w are constants.





b) prove that r X v is a constant (the cross product thing)


c) Show that the acceleration is directed toward the origin and is proportional to the distance from the orgin.





I worked out the second derivative (acceleation) to be - aw^2 cos (wt) - bw^2 sin (wt). I understand what a cross product is, but I thought it was used with points... I don't know how to cross product vectors.





Please help! Thanks in advance!

Question with vectors and cross products...?
v= dr/dt


v= -awsinwt + bwcoswt


rXv =abw(cos^2wt+sin^2wt) along +ive z axis


=abw


=constant








a=dv/dt


a= -aw^2coswt - bw^2sinwt


==%26gt; directed towards centre
Reply:When you take the cross-product with points you are actually taking the cross-product of the position vectors of the points. So you do know how to do it with vectors - have a bit of self-confidence.





Best of Luck - Mike
Reply:cross product: axb=|a|*|b|*sin(theta) where theta is the angle between the two vectors, |a| and |b| are the absolute values of a,b.





The velocity vector will always be tangential (theta=90 degrees) from the position vector r.





acceleration = -aw^2cost(wt)-bw^2sin(wt)


= w^2*(-acos(wt)-bsin(wt))


= (w^2)*(-1)*(r) notice that acos(wt)+bsin(wt)=r


thus the aceleration is proportional to r, the distance from the origin, scaled by w^2, and points towards the origin (acel is negative for positive r, positive for negative r).