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Show that the straight lines whose direction cosines are given by the equations `a l+b m+c n=0a n dul^2+z m^2=v n^2+w n^2=0` are parallel or perpendicular as `(a^2)/u+(b^2)/v+(c^2)/w=0ora^2(v+w)+b^2(w+u)+c^2(u+v)=0.`

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ML KHANNA-CO-ORDINATE GEOMETRY OF THREE DIMENSION-MISCELLANEOUS EXERCISE(TRUE AND FALSE)
  1. If a variable line in two adjacent position has direction cosines l,m,...

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  2. Find the angle between the lines whose direction cosines are connec...

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  3. Show that the straight lines whose direction cosines are given by t...

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  4. The equation of the plane through the points (1,1,1),(1,-1,1) and (-7,...

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  5. The equation of the plane through the points (2,2,1) and (9,3,6) and p...

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  6. The equation of the plane through the intersection of the planes x-2y+...

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  7. A variable plane at a constant distance p from the origin meets the ax...

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  8. A variable plane is at a constant distance p from the origin and meets...

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  9. A plane a constant distance p from the origin meets the coordinate axe...

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  10. The equation 2x^(2) -6y^(2) - 12z^(2)+18 yz +2zx + xy =0 represents a ...

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  11. The lines (x-1)/1=(y-2)/2=(z-3)/3 and x/2=(y+2)/2=(z-3)/-2 are paral...

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  12. The lines (x-1)/2=(y-2)/2=(z-3)/0 and (x-2)/0=(y+3)/0=(z-4)/1 are pa...

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  13. The plane x-2y+z-6=0 and the line x/1=y/2=z/3 are related as the line ...

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  14. Find the length of the perpendicular from point (3,4,5) on the line (x...

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  15. Find the angle between the lines in which the planes : 3x - 7y - 5z ...

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  16. The lines 2x+3y-4z=0 ,3x-4y+z=7 5x-y-3z+12=0, x-7y+5z-6=0 are parell...

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  17. The lines (x-5)/4=(y-7)/4=(z+3)/-5 and (x-8)/7=(y-4)/1=(z-5)/3 are cop...

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  18. A sphere of constant radius k , passes through the origin and me...

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  19. A variable plane passes through a fixed point (a ,b ,c) and cuts th...

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  20. If any tangent plane to the sphere x^(2) + y^(2) +z^(2) makes interc...

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