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Show that the lines (x+4)/3=(y+6)/5=(z-1...

Show that the lines `(x+4)/3=(y+6)/5=(z-1)/-2` and `3x-2y+z+5=0=2x+3y+4z-4` intersect. Find the equation of the plane in which they lie and also their point of intersection.

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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.

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PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Find the equation of the plane which is perpendicular to the plane 5 x...

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  2. Find the equation of the plane bisectiing the angles between the plane...

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

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  4. Prove that the line of section of the planes 5x+2y-4z+2=0 and 2x+8y+2z...

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  5. Find the equations of the line through the point (1,2,4) and parallel ...

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  6. Find the angle between the lines: x-2y+z=0=x+2y-2z and x+2y+z=0=3x+9y+...

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  7. Prove that the lines x=py+q, z=ry+s and x=p'y+q'z=r'y+s' are at right ...

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  8. Find the equations of the plane through the intersection of the planes...

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  9. Find the equations of the plane which contains the line of intersectio...

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  10. If a line makes angles of 90^@,60^@ and theta with the x, y and z axis...

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  11. Name the locus of the equation x^2+y^2=0.

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  12. What is the locus of the equations x^2+y^2+z^2=0?

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  13. Write the direction cosines of the Y-axis.

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  14. What is the shortest distance between two intersecting lines?

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  15. Direction cosines of hat i are ‘

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  16. Write down direction cosines of the line (1-x)/1=(y-2)/1=(z-3)/1.

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  17. What is the angle between the planes x+y=0 and z=0.

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  18. Name the surface represented by the equation ax+by+cz+d=0, where a^2+b...

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  19. Write the attitude numbers of the plane 2x-3y+4z-13=0.

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  20. Find p if the planes 2x+3y+6z-13=0 and 6x+py-3z=0 are at right angles.

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