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 vector product \(\vec{OP} \times \vec{v}\) is independent of the position \(P\) of the particle moving with constant speed \(\vec{v}\). Here’s a step-by-step solution:

### Step 1: Define the vectors
Let \(O\) be a fixed point in space, and let \(P\) be the position of the particle at any time \(t\). We can represent the position vector of point \(P\) relative to point \(O\) as:
\[ \vec{OP} = x \hat{i} + y \hat{j} \]
where \(x\) and \(y\) are the coordinates of point \(P\) in the Cartesian coordinate system.
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