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Find the vector equation of a plane whic...

Find the vector equation of a plane which is at a distance of 8 units from the origin and which is normal to the vector `2 hat i+ hat j+2 hat kdot`

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To find the vector equation of a plane that is at a distance of 8 units from the origin and is normal to the vector \( \mathbf{n} = 2\hat{i} + \hat{j} + 2\hat{k} \), we can follow these steps: ### Step 1: Identify the normal vector The normal vector to the plane is given as: \[ \mathbf{n} = 2\hat{i} + \hat{j} + 2\hat{k} \] ...
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RD SHARMA-THE PLANE -Solved Examples And Exercises
  1. Find the vector equation of the plane passing through the points A(a ,...

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  2. Reduce the equation vec rdot(3 hat i-4 hat j+12 hat k)=5 to normal fo...

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  3. Find the vector equation of a plane which is at a distance of 8 units ...

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  4. Find the direction cosines of perpendicular from the origin to the ...

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  5. Find the coordinates of the foot of the perpendicular drawn from the ...

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  6. Find the equation of a plane which is at a distance of 3sqrt(3) units ...

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

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  8. Find the vector equation of the plane passing through the points A(2,2...

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  9. Find the equation of the plane passing through the point (1,2,1) and p...

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  10. If from a point P(a ,b ,c) perpendiculars P Aa n dP B are drawn to Y Z...

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  11. Find the vector equation of the plane passing through the points havin...

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  12. Find the equation of the plane through the points P(1,\ 1,\ 0),\ Q(1,\...

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  13. Find the equation of the plane passing through the following points: (...

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  14. Find the equation of the plane passing through the following points: (...

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  15. Find the equation of the plane passing through the following points: (...

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  16. Find the equation of the plane passing through the following points: (...

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  17. Find the equation of the plane passing through the following points: (...

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  18. Show that the following points are coplanar: (0,\ -1,\ 0),\ (2,\ 1,\ -...

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  19. Show that the following points are coplanar: (0,\ 4,\ 3),\ (-1,\ -5,\ ...

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  20. Show that the point (0, -1, -1), (4 5, 1), (3, 9, 4) and (-4, 4, 4) ar...

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