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The ratio in which the line joining (2,4...

The ratio in which the line joining (2,4,5) and (3,5,-9) is divided by the yz-plane is a. 2:3            b. 3:2             c. -2:3           d. 4:3

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To find the ratio in which the line joining the points \( A(2, 4, 5) \) and \( B(3, 5, -9) \) is divided by the YZ-plane, we follow these steps: ### Step 1: Understand the YZ-plane The YZ-plane is defined by the equation \( x = 0 \). This means that any point on the YZ-plane will have its x-coordinate equal to zero. ### Step 2: Set up the coordinates Let the point where the line segment joining \( A \) and \( B \) intersects the YZ-plane be \( P(0, y, z) \). We need to find the ratio in which the point \( P \) divides the segment \( AB \). ...
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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 a point equidistant from the origin and pints ...

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

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

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

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  6. If the origin is the centroid of a triangle ABC having vertices A(a ,1...

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  7. The ratio in which the line joining (2,4,5) and (3,5,-9) is divided by...

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  8. The ratio in which the line joining the points (a , b , c)a n d\ (-a ,...

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  9. If P(0,1,2),\ Q(4,-2,1)a n d\ O(0,0,0) are three points then angle P ...

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  10. If the extremities of the diagonal fo a square are (1,-2,3) and (2,...

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  11. The points (5,-4,2), (4,-3,1), (7,6,4) and (8,-7,5) are the vertices o...

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  12. In a three dimensional space the equation x^2-5x+6=0 represents a. poi...

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  13. Let (3,4,-1) and (-1,2,3) be the end points of  diameter of a sphere. ...

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  14. XOZ-plane divides the join of (2,3,1) and (6,7,1) in the ratio a. 3:7...

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  15. What is the locus of a point for which y=0,\z =0? a. x-axis b. y-ax...

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  16. The coordinates of the foot of the perpendicular drawn from the point ...

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  17. The perpendicular distance of the point P(6,7,8) from xy-plane is a. 8...

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  18. The length of the perpendicular drawn from the point P(3,4,5) on y-axi...

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  19. The perpendicular distance of the point P(3,3,4) from the x-axis is 3s...

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  20. The length of the perpendicular drawn from the point P(a , b , c) fro...

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