At a certain instant, the velocity and acceleration of a particle ar defined by v= 3i + 4j - 6k m/s and a=-2i + 3k m/s2. Find the radius of curvature and change of speed of the particle at the instant.

 

feyma06,
In this case, break the acceleration vector into two components. One parallel to the velocity vector (tangential component), and the other perpendicular to it(normal component). The component of acceleration responsible for change in magnitude of velocity is the tangential one.
To find rate of change of speed take dot product of acc. with unit velocity vector.
The normal component is responsible for change in direction of velocity. To find radius of curvature, use the formula r = (magnitude of velocity) squared/ magnitude of normal component of acceleration vector.

hope this helps.