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Prove that the two lines whose direction...

Prove that the two lines whose direction cosines are connected by the relations `al+bm+cn=0 and u l^(2)+v m^(2)+w n^(2)=0` are perpendicular if `a^(2)(v+w)+b^(2)(w+u)+c^(2)(u+v)=0` and parallel if `(a^(2))/(u)+(b^(2))/(v)+(c^(2))/(w)=0`.

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PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. If the edges of a rectangular parallelopiped are a, b and c, show that...

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  2. Find the general solution of the following (1+sinx)dy=ydx

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  3. Prove that the two lines whose direction cosines are connected by the ...

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  4. Find the general solution of the following (1+secx)dy=y^2dx

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  5. Find the shortest distance between two lines whose vector equations ar...

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  6. Find the shortest distance between each of the following pair of lines...

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  7. Find the shortest distance between each of the following pair of lines...

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  8. Find the general solution of the following (sinx+cosx)dy=y(cosx-sinx)d...

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  9. Find the shortest distance between each of the following pair of lines...

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  10. Find shortest distance between lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-2)...

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  11. Determine whether or not the following paris of lines intersect: vecr=...

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  12. Determine whether or not the following paris of lines intersect: vecr=...

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  13. Determine whether or not the following paris of lines intersect: (x-1)...

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  14. Find the general solution of the following (1+x^2)dy=xydx

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  15. Find the general solution of the following (e^x+1)dy=y(e^x)dx

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  16. Show that the lines (x-1)/23=(y+1)/2=(z-1)/5 and (x-2)/4=(y-1)/3=(z+1)...

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  17. Write the vector equation of the following lines and hence find distan...

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  18. Find the normal unit vector to the plane x+2y+3z-6=0.

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  19. Find the unit vector perpendicular to the plane vecr.(6hati+3hatj-2hat...

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  20. Find the cartesian equation of the following planes: vecr.(hati+hatj+h...

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