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Prove that the line of section of the pl...

Prove that the line of section of the planes 5x+2y-4z+2=0 and 2x+8y+2z-1=0 is parallel to the plane 4x-2y-5z-2=0.

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Find the equation of the through to the line of intersection of the planes 3x-4y+5z=10 and 2x+2y-3z=4 and parallel to the lines x=2y=3z .

Find the equation of the plane through the line of intersection of the planes: x+3y-z+1=0 and x+y-2z+3=0 and perpendicular to the plane 3x-y-2z-4=0

Find the equation of the plane through the line of intersection of the planes 2x+3y-3z+1=0 and x+y-2z+3=0 and perpendicular to the plane 3x-y-2z-4=0 .

Prove that the line of section of the planes 2x-y+z=4 and 5x+7y+2z=0 meets the plane 3x+4y-2z+3=0 in a single point. Find the cooridnates of that point.

Find the equation of the plane passing through the line of intersection of the planes 2x-y=0 and 3z-y=0 and perpendicular to the plane 4x+5y-3z=8

Find the equation of the plane passing through the line of intersection of the planes 2x+y-z=3 and 5x-3y+4z=9 and parallel to the lines (x-1)/(2)=(y-3)/(4)=(z-5)/(5)

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PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Find the equation of the plane bisectiing the angles between the plane...

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

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

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

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  6. 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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  7. Find the equations of the plane through the intersection of the planes...

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

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

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

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

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

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

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  14. Direction cosines of hat i are ‘

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

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

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

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

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

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  20. Find lambda if the lines x/6=y/2=z/-3 and x/p=y/-6=z/2 are at right an...

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