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Find the equation of the line passing through the point (2, 1, 3) and perpendicular to the lines `(x-1)/1=(y-2)/2=(z-3)/3andx/(-3)=y/2=z/5`

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To find the equation of the line passing through the point (2, 1, 3) and perpendicular to the given lines, we can follow these steps: ### Step 1: Identify Direction Ratios of the Given Lines The equations of the two lines are given in symmetric form. We can extract their direction ratios. 1. For the first line: \[ \frac{x-1}{1} = \frac{y-2}{2} = \frac{z-3}{3} ...
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Find the equation of the line passing through the point (3,1,2) and perpendicular to the lines (x-1)/1=(y-2)/2=(z-3)/3 and x/(-3)=y/2=z/5

What is the equation of the line passing through the point (1,2,3) and perpendicular to the lines (x+1)/(1)=(y+2)/(2)=(z+3)/(3) and (x)/(-3)=(y)/(2)=(z)/(5) ?

Find the equation of a line passes through the point (-2,1) and perpendicular to the line 3x+y=5 .

Find the equation of the line passing through the point (1, 2, 3) and perpendicular to the lines (x-1)/(3)=(y-3)/(1)=(z-4)/(-5)and(x-1)/(1)=(y-2)/(2)=(z-3)/(3)

(i) Find the vector and cartesian equation of the line passing through the point (1,2,-4) and perpendicular to the two lines : (x - 8)/(3) = (y + 19)/(-16) = (z - 10)/(7) and (x - 15)/(3) = (y - 19)/(8) = (z - 5)/(-5) . (ii) Find the vector and cartesian equations of the line passing through the point (2,1,3) and perpendicular to the lines : (x -1)/(1) = (y -2)/(2) = (z - 3)/(3) and (x)/(-3) = (y)/(2) = (z)/(5) .

Find the equation of the line passing through the point ( 3, 1, 2) and perpendicualr to the lines (x - 1)/(1) = (y - 2) /(2) = ( z - 3) /(3) "and" ( x)/(-3) = (y)/(2) = (z)/(5) .

Find the equation of the line passing through the point (-1,2,3) and perpendicular to the lines (x)/(2)=(y-1)/(-3)=(z+2)/(-2) and (x+3)/(-1)=(y+3)/(2)=(z-1)/(3)

Find the vector equation of the line passing through the point (1,-1,2) and perpendicular to the plane 2x-y+3z-5=0

Find the Cartesian equations of the line passing through the point (-1, 3, -2) and perpendicular to the lines x/1=y/2=z/3a n d\ (x+2)/(-3)=(y-1)/2=(z+1)/5

Find the equations of the line passing through the point (-1, 2,1 ) and parallel to the line (2x-1)/4=(3y+5)/2=(2-z)/3dot

RD SHARMA-STRAIGHT LINE IN SPACE -Solved Examples And Exercises
  1. Find the angle between two lines, one of which was direction ratios 2,...

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  2. Find the equations of the line passing through the point (-1, 2,1 ) an...

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  3. Find the equation of the line passing through the point (2, 1, 3) and ...

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

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  5. Determine the equations of the line passing through the point (1, 2, -...

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  6. If the coordinates of the points A ,\ B ,\ C ,\ D\ b e\ (1,\ 2,\ 3),\ ...

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  7. Find the direction cosines of the line (x+2)/2=(2y-7)/6=(1-z)/(-3) . A...

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  8. Determine whether the following pair of lines intersect or not. v...

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  9. 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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  10. Show that the lines (x+1)/3=(y+3)/5=(z+5)/7 and (x-2)/1=(y-4)/3=(z-6)/...

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  11. Determine whether the following pair of lines intersect or not. v...

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  12. Find the equation of the perpendicular from point (3,-1,11) to line x...

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  13. Find the perpendicular distasnce of the point (1,0,0) from the lines (...

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  14. Find the coordinates of the foot of the perpendicular drawn from po...

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  15. find the foot of perpendicular form (0,2,7) to lien (x+2)/(-1)=(y-1)/3...

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  16. Find the equation of line passing through points A(0,6,- 9) and B(-3,-...

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  17. Find the shortest distance between the lines whose vector equations...

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  18. Find the shortest distance between the lines (x-1)/2=(y-2)/3=(z-3)/...

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  19. Find the shortest distance between the following pair of lines and ...

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  20. Find the shortest distance between the following lines: (x-3)/1=(y-5)/...

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