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Let l(1) and l(2) be the two skew lines....

Let `l_(1) and l_(2)` be the two skew lines. If P, Q are two distinct points on `l_(1)` and R, S are two distinct points on `l_(2)`, then prove that PR cannot be parallel to QS.

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To prove that the line segment PR cannot be parallel to the line segment QS, we start with the definitions and properties of skew lines. ### Step-by-Step Solution: 1. **Define the Skew Lines**: Let the skew lines \( l_1 \) and \( l_2 \) be represented as: \[ l_1: \vec{r} = \vec{A} + \lambda \vec{B} \quad \text{(1)} ...
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