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Show that the lines (x-1)/23=(y+1)/2=(z-...

Show that the lines `(x-1)/23=(y+1)/2=(z-1)/5` and `(x-2)/4=(y-1)/3=(z+1)/-2` do not intersect.

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Show that the lines: (x-1)/3=(y+1)/2=(z-1)/5 and (x-2)/4=(y-1)/3=(z+1)/-2 do not intersect.

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

Show that the lines : (x+1)/3=(y+3)/5=(z+5)/7 and (x-2)/1=(y-4)/3=(z-6)/5 intersect each other. Also find their point of intersection.

Show that the two lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-4)/5=(y-1)/2=z intersect each other . Find also the point of intersection.

Show that the lines (x+1)/-3=(y-3)/2=(z+2)/1 and x/1=(y-7)/-3=(z+7)/2 intersect. Find the point of intersection and the equaion of the plane contianing them.

Show that the two lines (x-5)/4=(y-7)/4=(z+3)/-5 and (x-8)/7=(y-4)/1=(z-5)/3 intersect each other . Find also the point of intersection.

Show that the lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-2)/3=(y-3)/4=(z-4)/5 are coplanar. Also find the equation of the plane containing the lines.

Show that the lines : (x-3)/2=(y+1)/-3=(z-2)/4 and (x+2)/2=(y-4)/4=(z+5)/2 are perpendicular to each other.

The line (x-x_1)/0=(y-y_1)/1=(z-z_1)/2 is

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Find the general solution of the following (1+x^2)dy=xydx

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

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

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

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

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

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  8. Find the cartesian equation of the following planes: vecr.(2hati-3hatj...

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

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  10. Find the equation of the line passing through the point with position ...

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  11. Find the general solution of the following (1+logx)xdy=ydx

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  12. Find the equation of the plane passing through the point (3,-3, 1) and...

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  13. Find the equation of a plane which bisects perpendicularly the line se...

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  14. Find the equation of the plane through the point (1,4,-2) and parallel...

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  15. If the line drawn from (4,-1,2) to the point (-3,2,3) meets a plane at...

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  16. Find the equation of the plane through (1,5,-2) and parallel to the pl...

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  17. The position vectors of two points A and B are 3 hati+hatj+2hatk and h...

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  18. Find the vector equations of the line passing through the point (1,-1,...

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  19. Find the vector equation of the line through the origin, which is perp...

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  20. The vector equation of a plane is vecr.(2hati+2hatj-hatk)=21, find the...

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