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Introduction to Three Dimensional Geometry Miscellaneous Exercise on Chapter 11 Solutions
- Q1: Find the angle between the lines whose direction ratios are $a, b, c$ and $b – c, c – a, a – b$.
- Q2: Find the equation of a line parallel to $x$-axis and passing through the origin.
- Q3: 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 $k$.
- Q4: 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 $\vec{r} = (-4\hat{i} - \hat{k}) + \mu(3\hat{i} - 2\hat{j} - 2\hat{k})$.
- Q5: 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 $\frac{x-15}{3} = \frac{y-29}{8} = \frac{z-5}{-5}$.
Other Exercises for CBSE - Class 11 Mathematics Introduction to Three Dimensional Geometry
Chapters in CBSE - Class 11 Mathematics
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