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

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