List of top Mathematics Questions on Distance between Two Lines asked in MHT CET

The shortest distance between the lines \(\frac{x-3}{3} = \frac{y-8}{-1} = \frac{z-3}{1}\) and \(\frac{x+3}{-3} = \frac{y+7}{2} = \frac{z-6}{4}\) is

The shortest distance between the lines \(\overset{⃗}{r} = (4\hat{i}-\hat{j})+λ(\hat{i}+2\hat{j}-3\hat{k})\) and \(\overset{⃗}{r} = (\hat{i}-\hat{j}+2\hat{k})+μ(\hat{i}+4\hat{j}-5\hat{k})\) is...

If \(p\) is the shortest distance between the lines \(\frac{x+1}{7} = \frac{y+1}{-6} = z+1\) and \(\overset{⃗}{r} = (3\hat{i}+5\hat{j}+7\hat{k})+μ(\hat{i}-2\hat{j}+\hat{k})\) then \([p]\) is... ,(where \([\,.\,]\) denotes the greatest integer function.)

The values of p and q so that the line joining the points (7, p, 2) and (q, -2, 5) may be parallel to the line joining the points (2, -3, 5) and (-6, -15, 11) are

The lines \(\frac{x-1}{-1} = \frac{y+2}{1} = \frac{z-3}{-2}\) and \(\frac{x-1}{1} = \frac{y+2}{1} = \frac{z+1}{-2}\) are

The shortest distance between the lines, where the first line passes through \((0,0,0)\) and \((2,0,3)\) and the second line passes through \((2,5,0)\) and \((0,4,0)\) is

Determine the shortest distance between the lines \( \dfrac{x-1}{2} = \dfrac{y-2}{3} = \dfrac{z-3}{4} \) and \( \dfrac{x-2}{3} = \dfrac{y-4}{4} = \dfrac{z-5}{5} \).

If the shortest distance between the lines $\frac{x - k}{2} = \frac{y - 4}{3} = \frac{z - 3}{4}$ and $\frac{x - 2}{4} = \frac{y - 4}{6} = \frac{z - 7}{8}$ is $\frac{13}{\sqrt{29}}$, then $k =$}

The lines $\vec{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(3\hat{i} - \hat{j})$ and $\vec{r} = (4\hat{i} - \hat{k}) + \mu(2\hat{i} + 3\hat{k})$ are \dots}

If the shortest distance between the lines $\bar{r}_1 = \alpha\hat{i} + 2\hat{j} + 2\hat{k} + \lambda(\hat{i} - 2\hat{j} + 2\hat{k}), \lambda \in \mathbb{R}, \alpha > 0$ and $\bar{r}_2 = -4\hat{i} - \hat{k} + \mu(3\hat{i} - 2\hat{j} - 2\hat{k}), \mu \in R$, is $9$, then the value of $\alpha$ is

If the shortest distance between the lines $\bar{r}_1 = \alpha\hat{i} + 2\hat{j} + 2\hat{k} + \lambda(\hat{i} - 2\hat{j} + 2\hat{k}), \lambda \in \mathbb{R}, \alpha > 0$ and $\bar{r}_2 = -4\hat{i} - \hat{k} + \mu(3\hat{i} - 2\hat{j} - 2\hat{k}), \mu \in R$, is $9$, then the value of $\alpha$ is

The shortest distance between lines $\vec{r} = (2\hat{i} - \hat{j}) + \lambda(2\hat{i} + \hat{j} - 3\hat{k})$ and $\vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \mu(2\hat{i} + \hat{j} - 5\hat{k})$ is

The distance between the parallel lines $\frac{x-2}{3}=\frac{y-4}{5}=\frac{z-1}{2}$ and $\frac{x-1}{3}=\frac{y+2}{5}=\frac{z+3}{2}$ is

The distance between parallel lines $\bar{r} = (2\hat{i} - \hat{j} + \hat{k}) + \lambda(2\hat{i} + \hat{j} - 2\hat{k})$ and $\bar{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \mu(2\hat{i} + \hat{j} - 2\hat{k})$ is

The distance between parallel lines $\bar{r} = (2\hat{i} - \hat{j} + \hat{k}) + \lambda(2\hat{i} + \hat{j} - 2\hat{k})$ and $\bar{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \mu(2\hat{i} + \hat{j} - 2\hat{k})$ is

If the shortest distance between the lines $\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{\lambda}$ and $\frac{x - 2}{1} = \frac{y - 4}{4} = \frac{z - 5}{5}$ is $\frac{1}{\sqrt{3}}$, then sum of possible values of $\lambda$ is