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Using section formula, show that the poi...

Using section formula, show that the points `A(2,-3,4),\ B(-1,2,1)\ a n d\ C(0,1/3,2)\ ` are collinear.

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Let, C divides AB in the ratio `λ:1` Then, the coordinates of C are
`((-lambda+2)/(lambda+1) , (2lambda+3)/(lambda+1), (-lambda+4)/(lambda+1))`
But the coordinates of C are `(0,1/3,2)`
...
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RD SHARMA-INTRODUCTIONS TO 3-D COORDINATE GEOMETRY-Solved Examples And Exercises
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  2. Find the coordinates of the points which tisect the line segment jo...

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  3. Using section formula, show that the points A(2,-3,4),\ B(-1,2,1)\ a n...

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  4. Given that P(3,2,-4),\ Q(5,4,-6)a n d\ R(9,8,-10) are collinear. Find ...

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  5. Find the ratio in which the segment joining the points (4,8,10) and ...

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  6. Write the distance of the point P(2,3,5) from the xy-plane.

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  7. Write the distance of the point P(3,4,5) from z-axis.

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  8. If the distance between the points P(a ,2,1)a n d\ Q(1,-1,1) is 5 unit...

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  9. The coordinates of the mid points of sides AB, BC and CA of A B C are...

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  11. Write the length of the perpendicular drawn from the point P(3,5, 12) ...

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  12. Write the coordinates of third vertex of a triangle having centroid at...

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  13. What is the locus of a point (x , y , z) for which y=0, z=0?

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  14. Find the ratio in which the line segment joining the points (2,4,5) an...

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  15. Find the point on y-axis which is at a distance of sqrt(10) units from...

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  16. Find the point on x-axis which is equidistant from the points A(3,2,2)...

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  17. Find the coordinates of a point equidistant from the origin and pints ...

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  18. Write the coordinates of the point P which is five sixth of the way fr...

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  19. If a parallelepiped is formed by the planes drawn through the points ...

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  20. Determine the point on yz-plane which is equidistant from points A(2,0...

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