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

Show that the points (2, 3, 4), (– 1, – 2, 1), (5, 8, 7) are collinear.

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MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. Find the direction cosine of a line which makes equal angles with the ...

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  2. If a line has the direction ratios –18, 12, – 4, then what are its dir...

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  3. Show that the points (2, 3, 4), (– 1, – 2, 1), (5, 8, 7) are collinear...

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  4. Find the direction cosines of the sides of the triangle whose vertices...

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  5. show that the three lines with direction cosines <12/13,-3/13,-4/13>, ...

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  6. Show that the line through the points (1, – 1, 2), (3, 4, – 2) is perp...

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  7. Show that the line through the points : (4,7,8), (2,3,4) is parallel t...

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  8. Find the equation of the line which passes through the point (1, 2, 3)...

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  9. Find the equation of the line in vector and in cartesian form that pas...

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  10. Find the cartesian equation of the line which passes through the point...

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  11. The cartesian equation of a line is (x-5)/3 = (y+4)/7 = (z-6)/2. Write...

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  12. Find the vector and the cartesian equations of the lines that passes t...

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  13. Find the vector and the cartesian equations of the line that passes th...

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  14. Find the angle between the following pair of lines: vecr = 2hati-5hatj...

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  15. Find the angle between the following pair of lines: vecr = 3hati+hatj-...

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  16. Find the angle between the following pairs of lines : (x-2)/2=(y-1)/5=...

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  17. Find the angle between the lines x/2=y/2=z/1 and [x-5]/4=[y-2]/1=[z-3]...

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  18. Find the value of p so that the lines : l1:(1-x)/3=(7y-14)/(2p)=(z-3)/...

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  19. Show that the lines (x-5)/7 = (y+2)/-5 = z/1 and x/1 = y/2 = z/3 are p...

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  20. Find the shortest distance between the lines vecr = (hati + 2hatj+hatk...

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