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Prove that the lines x=py+q, z=ry+s and ...

Prove that the lines x=py+q, z=ry+s and x=p'y+q'z=r'y+s' are at right angles if pp'+rr'+1=0.

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PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Find the equations of the line through the point (1,2,4) and parallel ...

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

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  3. 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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  4. Find the equations of the plane through the intersection of the planes...

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

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

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

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

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

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

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  11. Direction cosines of hat i are ‘

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

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

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

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

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

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  17. 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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  18. Find the intercepts of the plane 2x-3y+4z-24=0 on the cooridnate axes.

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  19. Find the distance of the plane x+y+z-sqrt3=0 from the origin.

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  20. Does the line x=y=0 lie in the plane z=0.

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