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Prove that the lines x=az+b,y=cz+d and x...

Prove that the lines `x=az+b,y=cz+d` and `x=a_1z + b_1,y=c_1z+d_1 ` are perpendicular if `aa_1+"cc"_1+1=0.`

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ARIHANT PUBLICATION-THREE-DIMENSIONAL GEOMETRY-Odisha Bureau.s Textbooks Solutions (Exercise 13(c)) (True (T) or False (F))
  1. Find the equation of the line through the point (3, -1, 2) and paralle...

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  2. Obtain the equation of the line through the point (1, 2, -3) and perpe...

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  3. Prove that the lines x=az+b,y=cz+d and x=a1z + b1,y=c1z+d1 are perpen...

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  4. Find the points of intersection of the line (x-1)/1=(y+2)/ 3 =(z-1)/(...

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  5. Find the co-ordinates of the point where the line joining (3,4,-5) and...

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  6. Find the distance of the point (-1,-5,-10) from the point of intersect...

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  7. Find the image of the point (2,-1,3) in the plane 3x-2y+z-9=0

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

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  9. Prove that the lines (x+4)/3=(y+6)/5=(z-1)/(-2) and 3x-2y+z+5=0=2x+3y...

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  10. Show that the lines 7x - 4y + 7z +16 = 0 = 4x + 3y - 2z + 3 and x - 3y...

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  11. Show that the line joining the points (0,2,-4) and (-1,1-2) and the l...

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  12. Show that the line (x-1)/(1) = (y+2)/(3) = (z-1)/(-1) lies on the plan...

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  13. Find the angle between the plane x+y+4=0 and the line (x+3)/2=(y-1)/1=...

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  14. Find the angle betweenthe plane 4x+3y+5z-1=0 and line (x+3)/2=(y-1)/3=...

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  15. Find the equation of the line passing through the point (1, 0, -1) and...

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  16. A line with direction ratios lt2,1,2gt meets each of the lines x=y+a=z...

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  17. Obtain the co-ordinates of the foot of the perpendicular drawn from th...

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  18. Find the perpendicular distance of the point (-1,3,9) from the line (x...

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  19. Find the distance of the point (1,-2,3) from the plane x-y+z=5, measur...

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  20. Find the distance of the point (1,-1,-10) from the line (x-4)/1=(y+3)/...

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