List of top Mathematics Questions on Distance between parallel lines

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.
The ratio in which the line \( 3x + 4y + 2 = 0 \) divides the distance between the lines \( 3x + 4y + 5 = 0 \) and \( 3x + 4y - 5 = 0 \) is