Question

Opposite sides of a square are along the lines : \[ \vec{r} = \hat{i} + 2\hat{j} - 4\hat{k} + \lambda(2\hat{i} + 3\hat{j} + 6\hat{k}) \quad \text{and} \quad \vec{r} = 3\hat{i} + 3\hat{j} - 5\hat{k} + \mu(2\hat{i} + 3\hat{j} + 6\hat{k}) \] 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 $p$.

Hint:

Always double check vector components during cross-product evaluations. Finding the distance between parallel lines gives you the exact side length of the square, and squaring it gives the total area directly.

Answer 1