If `vecPxxvecQ=vecRxxvecQ`, is `vecR=vecP` always ?

Explanation

To determine whether \(\vec{R} = \vec{P}\) always holds true given that \(\vec{P} \times \vec{Q} = \vec{R} \times \vec{Q}\), we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Cross Product**:
The cross product of two vectors \(\vec{A}\) and \(\vec{B}\) is given by:
\[
\vec{A} \times \vec{B} = |\vec{A}| |\vec{B}| \sin(\theta) \hat{n}
...