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CBSE - Class 11 > Mathematics > Introduction to Three Dimensional Geometry Worksheets

Free CBSE - Class 11 Mathematics - Introduction to Three Dimensional Geometry worksheets

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1.
Show that the lines $\frac{x-5}{7} = \frac{y+2}{-5} = \frac{z}{1}$ and $\frac{x}{1} = \frac{y}{2} = \frac{z}{3}$ are perpendicular to each other.
2.
Find the shortest distance between the lines $\vec{r} = (\hat{i} + 2\hat{j} + \hat{k}) + \lambda(\hat{i} - \hat{j} + \hat{k})$ and $\vec{r} = (2\hat{i} - \hat{j} - \hat{k}) + \mu(2\hat{i} + \hat{j} + 2\hat{k})$
3.
Find the shortest distance between the lines $\frac{x+1}{7} = \frac{y+1}{-6} = \frac{z+1}{1}$ and $\frac{x-3}{1} = \frac{y-5}{-2} = \frac{z-7}{1}$
4.
Find the shortest distance between the lines whose vector equations are $\vec{r} = (\hat{i} + 2\hat{j} + 3\hat{k}) + \lambda(\hat{i} - 3\hat{j} + 2\hat{k})$ and $\vec{r} = (4\hat{i} + 5\hat{j} + 6\hat{k}) + \mu(2\hat{i} + 3\hat{j} + \hat{k})$
5.
Find the shortest distance between the lines whose vector equations are $\vec{r} = (1-t)\hat{i} + (t-2)\hat{j} + (3-2t)\hat{k}$ and $\vec{r} = (s+1)\hat{i} + (2s-1)\hat{j} - (2s+1)\hat{k}$
6.
Find the angle between the lines whose direction ratios are $a, b, c$ and $b – c, c – a, a – b$.
7.
Find the equation of a line parallel to $x$-axis and passing through the origin.
8.
If the lines $\frac{x-1}{-3} = \frac{y-2}{2k} = \frac{z-3}{2}$ and $\frac{x-1}{3k} = \frac{y-1}{1} = \frac{z-6}{-5}$ are perpendicular, find the value of $k$.
9.
Find the shortest distance between lines $\vec{r} = (6\hat{i} + 2\hat{j} + 2\hat{k}) + \lambda(\hat{i} - 2\hat{j} + 2\hat{k})$ and $\vec{r} = (-4\hat{i} - \hat{k}) + \mu(3\hat{i} - 2\hat{j} - 2\hat{k})$.
10.
Find the vector equation of the line passing through the point (1, 2, – 4) and perpendicular to the two lines: $\frac{x-8}{3} = \frac{y+19}{-16} = \frac{z-10}{7}$ and $\frac{x-15}{3} = \frac{y-29}{8} = \frac{z-5}{-5}$.
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Chapters in CBSE - Class 11 Mathematics

Mathematics Worksheet Sets Worksheet Relations and Functions Worksheet Trigonometric Functions Worksheet Complex Numbers Worksheet Linear Inequalities Worksheet Permutations and Combinations Worksheet Binomial Theorem Worksheet Sequences and Series Worksheet Straight Lines Worksheet Conic Sections Worksheet Limits and Derivatives Worksheet Statistics Worksheet Probability Worksheet

Free Introduction to Three Dimensional Geometry Worksheets

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Rahul Verma Introduction to Three Dimensional Geometry in Delhi

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