List of top Mathematics Questions on Distance between Two Lines asked in CBSE Class XII

In a school, the swimming pool is shaped as a cuboid, and the breadth of the pool is represented by line \(\frac{-x+2}{-5} = y = z-3\). Two students A and B are swimming along the length of the pool.

Based on the above information, answer the following questions :

(iii) (b) If a bird flies across the top of the swimming pool with its path represented by \(\frac{x+4}{2}=\frac{y+3}{8}=\frac{z-5}{-18}\), then find the shortest distance between its path and the path of student A.

Check whether the lines given by \(\dfrac{x-1}{2} = \dfrac{y-2}{3} = \dfrac{z-3}{4}\) and \(\dfrac{x-4}{5} = \dfrac{y-1}{2} = z\) are parallel or not. If parallel, find the distance between them, otherwise find their point of intersection, if the lines are intersecting.

Find:

The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]