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Find the equations of the two lines thro...

Find the equations of the two lines through the origin which intersect the line `(x-3)/2=(y-3)/1=z/1` at angle of `pi/3` each.

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AI Generated Solution

To find the equations of the two lines through the origin that intersect the line \((x-3)/2 = (y-3)/1 = z/1\) at an angle of \(\pi/3\), we can follow these steps: ### Step 1: Write the given line in parametric form The given line can be expressed in terms of a parameter \(\lambda\): \[ x = 2\lambda + 3, \quad y = \lambda + 3, \quad z = \lambda \] ...
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RD SHARMA-STRAIGHT LINE IN SPACE -Solved Examples And Exercises
  1. Find the direction cosines of teh line (x-2)/2=(2y-5)/(-3),z=-1. Also,...

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  2. Show that the lines (x-1)/3=(y+1)/2=(z-1)/5a n d(x+2)/4=(y-1)/3=(z+1)/...

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  3. Find the equations of the two lines through the origin which inters...

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  4. Find the vector of a line passing through (2,-1,1) and parallel to the...

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  5. The Cartesian equations of a line are x=a y+b ,z=c y+ddot Find its dir...

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  6. By computing the shortest distance determine whether the following p...

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  7. Find the proof of perpendicular from the point (2,3,4) to the line (4-...

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  8. Find the image of the point (1,6,3) in the line x/1=(y-1)/2=(z-2)/3 . ...

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  9. Show that the distance d from point P to the line l having equation v...

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  10. Find the angle between two lines whose direction ratios are proport...

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  11. Find the angle between the lines (x-2)/3=(y+1)/(-2),z=2 " " "and" " " ...

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  12. Find the angle between the lines vec r=3 hat i+2 hat j-4 hat k+lambda...

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  13. Find the vector equation of a line passing through the point with p...

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  14. Find the vector equation of the line passing through the point (2,-...

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  15. Find the equation of the line passing through the point (1,-1,1) an...

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  16. Find the equation of the line passing through the point hat i+ ha...

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  17. Find the equation of a line passing through (1,-1,0) and parallel to t...

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  18. Vertices Ba n dC of A B C lie along the line (x+2)/2=(y-1)/1=(z-0)/4 ...

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  19. Find the distance from the point P(3,8,1) to the line (x-3)/3=(y+7)/(...

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  20. Show that the line (x-1)/2=(y-2)/3=(z-3)/4a n d(x-4)/5=(y-1)/2 inters...

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