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Show that the points A (2, 3, 4), B (1,...

Show that the points `A (2, 3, 4)`, `B (1, 2, 3)`and `C (3, 8, 11)`are collinear.

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the given points are `(2,3,4),(1,2,3),(3,8,11)`
thus,
For AB,
direction ratios are, `-1,-1,-1`
For AC,
direction ratios are, `1,5,7`
Now, the ratios are proportional
thus, A is common point
...
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NCERT-THREE DIMENSIONAL GEOMETRY-SOLVED EXAMPLES
  1. Find the vector equation for the line passing through the points (1, 0...

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  2. Find the vector and the Cartesian equations of the line through the p...

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  3. Show that the points A (2, 3, 4), B (1, 2, 3)and C (3, 8, 11)are co...

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  4. Find the direction cosines of x, y and z-axis.

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  5. Find the direction cosines of the line passing through the two points...

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  6. If a line has direction ratios 2,1,2.determine its direction cosines.

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  7. If a line makes angle 90^@, 60^@and 30^@with the positive direction ...

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  8. Find the angle between the pair of lines given by vecr=3 hat i+2 ha...

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  9. The Cartesian equation of a line is (x+3)/2=(y-5)/4=(z+6)/2. Find th...

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  10. Show that the lines (x+3)/(-3)=(y-1)/1=(z-5)/5and (x+1)/(-1)=(y-2)/2=(...

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  11. Find the vector equation of the plane passing through the intersectio...

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  12. Find the angle between the two planes 3x - 6y + 2z = 7and 2x + 2y - 2...

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  13. Find the angle between the two planes 2x + y 2z = 5and 3x 6y 2z = ...

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  14. Find the distance of a point (2, 5, 3)from the plane vecr.(6 hat i-...

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  15. Find the angle between the pair of lines (x+3)/3=(y-1)/5=(z+3)/4and (x...

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  16. Find the shortest distance between the lines l1 and l2 whose vector ...

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  17. Find the distance between the lines l1 and l2 given by r1= hat i+2 h...

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  18. Find the vector equation of the plane which is at a distance of 6/(sq...

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  19. Find the direction cosines of the unit vector perpendicular to the pla...

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  20. Find the distance of the plane 2x 3y + 4z 6 = 0from the origin.

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