Assertion $(A)$: For the lines $\overline{r}=\overline{a}+t \overline{b}$ and $\overline{r}=\overline{p}+s \overline{q}$,if $(\bar{a}-\bar{p}) \cdot(\bar{b} \times \bar{q}) \neq 0$,then the two lines are coplanar.
Reason $(R)$: $|(\bar{a}-\bar{p}) \cdot(\bar{b} \times \bar{q})|$ is $|\bar{b} \times \bar{q}|$ times the shortest distance between the lines $\overline{r}=\overline{a}+t\bar{b}$ and $\overline{r}=\overline{p}+s \overline{q}$.

  • A
    $A$ is true,$R$ is true and $R$ is the correct explanation to $A$
  • B
    $A$ is true,$R$ is true and $R$ is not the correct explanation to $A$
  • C
    $A$ is true,$R$ is false
  • D
    $A$ is false,$R$ is true

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