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Find the ratio in which the plane ax+by+...

Find the ratio in which the plane ax+by+cz+d=0 divides the join of the points `P(x_1,y_1,z_1)` and `Q(x_2,y_2,z_2)` lying on the plane. Hence, show that the points P(1,-2,3) and Q(0,0,-1) lie on opposite sides of the plane 2x+5y+7z=3.

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PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Find the distance of the line (x+1)/-3=(y-3)/2=(z-2)/1 in the plane x+...

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  2. The image of the line (x-1)/3=(y-3)/1=(z-4)/(-5) in the plane 2x-y+z...

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  3. Find the ratio in which the plane ax+by+cz+d=0 divides the join of the...

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  4. Show that the lines (x-a+d)/(alpha-delta) = (y-a)/alpha = (z-a-d)/(alp...

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  5. Find the angle between the planes 2x-3y+4z=1 and -x+y=4.

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  6. Find the angle between the planes: vecr.(hati+hatj)=1 and vecr.(hati+h...

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  7. Find the angle between the two planes 3x-6y+2z = 7 and 2x+2y-2z = 5

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  8. Show that the plane passing through the points (1,1,1), (1,-7,1) and (...

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  9. Find the equation of the plane passing through the points (1,-1,2) and...

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  10. Find the equation of the plane passing through the points (-1,1,1) and...

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  11. Find the equation of the plane passing through the line (x-1)/2=(y+1)/...

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  12. Obtain the equation of the plane passing through the point (1,-3,-2) a...

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  13. Find the angles between the line vecr=-hati+hatj+2hatk+lambda(3hati+2h...

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  14. Find the co-ordinates of the point, where the line: (x-2)/3=(y+1)/4=(z...

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  15. The distance of the point (2,1,-1) from the plane x-2y+4z=9 is :

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  16. Find the distance between the point (7,2,4) and the plane determined b...

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  17. Find the equations of two planes through the point (4,2,1),(2,1,-1) an...

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  18. Find the length of the projection of the line segment joining the poin...

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  19. Show that the line L whose vector equation is vecr=2hati-2hatj+3hatk+l...

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  20. Find the equation of plane passing through the point (1,4,-2) and para...

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