List of top Mathematics Questions on Distance between parallel lines asked in CBSE Class XII

Opposite sides of a square are along the lines :
$\vec{r} = \hat{i} + 2\hat{j} - 4\hat{k} + \lambda(2\hat{i} + 3\hat{j} + 6\hat{k})$
$\vec{r} = 3\hat{i} + 3\hat{j} - 5\hat{k} + \mu(2\hat{i} + 3\hat{j} + 6\hat{k})$
Find the area of the square if direction ratios of other pair of opposite sides of the square are given by $\langle -3, 6, p \rangle$. Also, find the value of $p$.}

Show that line \( AB \) passing through points \( A(0, 4, 1), B(2, 3, -1) \) and the line \( CD \) passing through points \( C(4, 5, 0), D(2, 6, 2) \) are parallel. Also, find distance between them.