Chapter 11 – 3D Geometry
Example 11 Find the shortest distance between the lines l 1 and l 2 whose vector equations are
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Nov
Example 11 Find the shortest distance between the lines l 1 and l 2 whose vector equations are Example 11 Find the shortest distance between the lines l 1 and l 2 whose vector equations are November 15, 2021 Category: Chapter 11 - 3D Geometry , Maths , NCERT Exemplar Class 12 ,
Example 10 Find the angle between the pair of lines x + 3/3 = y – 1/5 = z + 3/4 and x + 1/1 = y-4/1 = z – 5/2
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Nov
Example 10 Find the angle between the pair of lines x + 3/3 = y – 1/5 = z + 3/4 and x + 1/1 = y-4/1 = z – 5/2 Example 10 Find the angle between the pair of lines x + 3/3 = y - 1/5 = z + 3/4 and x + [...]
Example 9 Find the angle between the pair of lines given by r = 3i + 2j – 4k + lamba (i + 2j + 2k)
15
Nov
Example 9 Find the angle between the pair of lines given by r = 3i + 2j – 4k + lamba (i + 2j + 2k) Example 9 Find the angle between the pair of lines given by r = 3i + 2j - 4k + lamba (i + 2j + 2k) November 15, 2021 [...]
Example 8 The Cartesian equation of a line is Find the vector equation for the line.
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Nov
Example 8 The Cartesian equation of a line is Find the vector equation for the line. Example 8 The Cartesian equation of a line is Find the vector equation for the line. November 15, 2021 Category: Chapter 11 - 3D Geometry , Maths , NCERT Exemplar Class 12 ,
Example 7 Find the vector equation for the line passing through the points (–1, 0, 2) and (3, 4, 6).
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Nov
Example 7 Find the vector equation for the line passing through the points (–1, 0, 2) and (3, 4, 6). 2) and (3 4 6 Example 7 Find the vector equation for the line passing through the points (–1 November 15, 2021 Category: Chapter 11 - 3D Geometry , Maths , NCERT Exemplar Class 12 [...]
Example 6 Find the vector and the Cartesian equations of the line through the point (5, 2, – 4) and which is parallel to the vector 3i + 2j – 8k .
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Nov
Example 6 Find the vector and the Cartesian equations of the line through the point (5, 2, – 4) and which is parallel to the vector 3i + 2j – 8k . – 4) and which is parallel to the vector 3i + 2j - 8k . 2 Example 6 Find the vector and the [...]
Example 5 Show that the points A (2, 3, – 4), B (1, – 2, 3) and C (3, 8, – 11) are collinear.
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Nov
Example 5 Show that the points A (2, 3, – 4), B (1, – 2, 3) and C (3, 8, – 11) are collinear. – 11) are collinear. 2 3) and C (3 3% 4 8 B(-1 Example 5 Show that the points A (2 November 15, 2021 Category: Chapter 11 - 3D Geometry , [...]
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– 11) are collinear. ,
2 ,
3) and C (3 ,
3% ,
4 ,
8 ,
B(-1 ,
Example 5 Show that the points A (2 ,
Example 4 Find the direction cosines of x, y and z-axis.
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Nov
Example 4 Find the direction cosines of x, y and z-axis. Example 4 Find the direction cosines of x y- and z-axis November 15, 2021 Category: Chapter 11 - 3D Geometry , Maths , NCERT Exemplar Class 12 ,
Example 3 Find the direction cosines of the line passing through the two points (– 2, 4, – 5) and (1, 2, 3).
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Nov
Example 3 Find the direction cosines of the line passing through the two points (– 2, 4, – 5) and (1, 2, 3). 2 3% 4 5) and (–1 Example 3 Find the direction cosines of the line passing through the two points (– 2 November 15, 2021 Category: Chapter 11 - 3D Geometry , [...]
Example 2 If a line has direction ratios 2, – 1, – 2, determine its direction cosines.
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Nov
Example 2 If a line has direction ratios 2, – 1, – 2, determine its direction cosines. 1 2 determine its direction cosines. Example 2 If a line has direction ratios 2 November 15, 2021 Category: Chapter 11 - 3D Geometry , Maths , NCERT Exemplar Class 12 ,