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Class 12 Maths Practice Test - Shortest Distance between Two Lines
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Class 12 Maths Practice Test - Shortest Distance between Two Lines
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10 Questions

1. Find the shortest distance between two lines l1 and l2 whose vector equations is given below.
\(\vec{r}=3\hat{i}-4\hat{j}+2\hat{k}+λ(4\hat{i}+\hat{j}+\hat{k})\)
\(\vec{r}=5\hat{i}+\hat{j}-\hat{k}+μ(2\hat{i}-\hat{j}-3\hat{k})\)
2. Find the shortest distance between the lines given.
l1:\(\frac{x-5}{2}=\frac{y-2}{5}=\frac{z-1}{4}\)
l2:\(\frac{x+4}{3}=\frac{y-7}{6}=\frac{z-3}{7}\)
3. Find the equation between the two parallel lines l1 and l2 whose equations is given below.
\(\vec{r}=3\hat{i}+2\hat{j}-\hat{k}+λ(3\hat{i}-2\hat{j}+\hat{k})\)
\(\vec{r}=2\hat{i}-\hat{j}+\hat{k}+μ(3\hat{i}-2\hat{j}+\hat{k})\)
4. Find the shortest distance between the following set of parallel lines.
\(\vec{r}=6\hat{i}+2\hat{j}-\hat{k}+λ(\hat{i}+2\hat{j}-4\hat{k})\)
\(\vec{r}=\hat{i}+\hat{j}+\hat{k}+μ(\hat{i}+2\hat{j}-4\hat{k})\)
5. Find the shortest distance between the set of parallel lines.
\(\vec{r}=(\hat{i}+2\hat{j}-\hat{k})+λ(\hat{i}+\hat{j}+\hat{k})\)
\(\vec{r}=(3\hat{i}-\hat{j}+3\hat{k})+μ(\hat{i}+\hat{j}+\hat{k})\)
6. Find the distance between the lines l1 and l2 with the following vector equations.
\(\vec{r}=2\hat{i}+2\hat{j}-2\hat{k}+λ(3\hat{i}+2\hat{j}+5\hat{k})\)
\(\vec{r}=4 \hat{i}-\hat{j}+5\hat{k}+μ(3\hat{i}-2\hat{j}+4\hat{k})\)
7. Find the equation between the two parallel lines l1 and l2 whose equations is given below.
\(\vec{r}=3\hat{i}+2\hat{j}-\hat{k}+λ(3\hat{i}-2\hat{j}+\hat{k})\)
\(\vec{r}=2\hat{i}-\hat{j}+\hat{k}+μ(3\hat{i}-2\hat{j}+\hat{k})\)
8. Find the distance between the lines l1 and l2 with the following vector equations.
\(\vec{r}=2\hat{i}+2\hat{j}-2\hat{k}+λ(3\hat{i}+2\hat{j}+5\hat{k})\)
\(\vec{r}=4 \hat{i}-\hat{j}+5\hat{k}+μ(3\hat{i}-2\hat{j}+4\hat{k})\)
9. Find the shortest distance between the lines given.
l1:\(\frac{x-5}{2}=\frac{y-2}{5}=\frac{z-1}{4}\)
l2:\(\frac{x+4}{3}=\frac{y-7}{6}=\frac{z-3}{7}\)
10. Which of the below given is the correct formula for the distance between two skew lines l1 and l2?

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