# Position and acceleration vector - parallel and perpendicular

1. Feb 22, 2012

### logearav

Position and acceleration vector -- parallel and perpendicular

1. The problem statement, all variables and given/known data

The motion of a particle is defined by the position vector
r = A(Cos t + t Sin t) i + A(Sin t + t Cos t) j where t is expressed in seconds. Determine the values of t for which the position vector and acceleration vector are
a) perpendicular
b) parallel

2. Relevant equations

3. The attempt at a solution
For acceleration i have differentiate r twice and arrive at the equation. So, i should go for cross product to find 't' when they are parallel and dot product when they are perpendicular.
Am I right in my procedure, revered members?

2. Feb 22, 2012

### Staff: Mentor

Re: Position and acceleration vector -- parallel and perpendicular

Your proposed method looks fine, but is the given position vector correct? It doesn't appear to me that the position and acceleration vector will ever be perpendicular or parallel for a real value of t.

3. Feb 22, 2012

### logearav

Re: Position and acceleration vector -- parallel and perpendicular

Thanks gneill. But this is how the question appears in University Exam paper.