# Position and acceleration vector - parallel and perpendicular

Position and acceleration vector -- parallel and perpendicular

## Homework Statement

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

## 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?

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gneill
Mentor

## Homework Statement

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

## 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?
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.

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