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

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

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The correct Answer is:
`therefore` pp'+rr'+1=0
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KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-SOLUTION OF NCERT EXAMPLAR PROBLEMS (Short Answer Type Question)
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  3. Prove that the lines x = py + q, z = ry + s and x = p'y + q', z = r'y ...

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  4. Find the equation of a plane which bisects perpendicularly the line jo...

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  5. Find the equation of a plane which is at a distance 3sqrt3 units from ...

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  6. If the line drawn from the point (-2, -1, -3) meets a plane at right a...

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  7. Find the equation of the plane through the points (2, 1, 0), (3, -2, -...

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  8. Find the equations of the two lines through the origin which intersect...

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  9. Find the angle between the lines whose direction cosines are given by ...

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  10. If a variable line in two adjacent positions has direction cosines l, ...

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  11. If O is the origin and A is (a, b, c), then find the direction cosines...

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  12. Two systems of rectangular axis have the same origin. If a plane cuts ...

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  13. Find the foot of perpendicular from the point (2, 3, -8) to the line (...

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  14. Find the distance of a point (2, 4, -1) from the line (x+5)/(1)=(y+3)/...

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  15. Find the length and the foot of perpendicular from the point (1,3/2,2)...

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  16. Find the equation of the line passing through the point (3, 0, 1) and ...

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  17. Find the equation of the plane through the points (2, 1,-1) and (-1, 3...

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  18. Find the shortest distance between the lines vecr =(8+3lambda) hati - ...

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  19. Find the equation of the plane which is perpendicular to the plane 5x ...

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  20. If the plane ax + by = 0 is rotated about its line of intersection wit...

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