A particle moves on a given straight line with a constant speed v. At a certain time it is at a point P on its straight lline path.O is a fixed point. Show than `vec(OP)xxvec upsilon` is independent of the position P.?

Explanation

To solve the problem, we need to show that the cross product of the position vector \(\vec{OP}\) and the velocity vector \(\vec{v}\) is independent of the position \(P\) of the particle moving along a straight line with constant speed \(v\).

### Step-by-Step Solution:

1. **Define the Position Vector \(\vec{OP}\)**:
Let the fixed point \(O\) be at coordinates \((0, y)\) in a 2D plane, where \(y\) is a constant height. The particle \(P\) moves along the x-axis at a distance \(x\) from the origin. Therefore, the position vector \(\vec{OP}\) can be expressed as:
\[
\vec{OP} = x \hat{i} + y \hat{j}
...