1. The problem statement, all variables and given/known data A particle moves along any path in 3d space with constant speed. Show that its velocity and accelerations vectors must always be perpendicular to each other.[hint. Differentiate the formula v dot v = v^2 with respect to t. 2. Relevant equations possible equations: v=dr/dt=dr/ds*ds/dt, a=dv/dt=(dv/dt)t +(v^2/rho)n, v=v*t where t is the unit tangent vector and n is the normal unit vector. 3. The attempt at a solution If a particle is moving in 3d space with constant speed, then the type of motion could be uniform circular motion and the acceleration is therefore equal to zero. Probably, v dot v= v^2(x) + v^2(y)+ v^2(z) , x , y and z making up the dimensions of the 3-D plane; since the particle moves along a 3D plane. If the particle is in uniform motion, the position vector r probably is in polar coordinates: r= b*cos(theta)i + b*sin(theta)j and theta is equal to ut/b where u is the speed of the particle , b is the arc length and t is the time its traveled. Would I differentiate r and then plugged in dr/dt into the v dot v equation? I expect I also have to show that x hat times y hat or x hat times z hat or y hat times z is equal to zero, since the problem asks me to show that velocity and acceleration vectors are always perpendicular to each other. Maybe the simplest solution is to show that v cross a = 0 since the acceleration of the particle is zero and therefore I would be done with the problem.