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Find the Cartesian form of equation of a plane whose vector equation is : ` vec rdot((- hat i+ hat j+2 hat k)=9`

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To find the Cartesian form of the equation of a plane given its vector equation, we can follow these steps: ### Step 1: Understand the given vector equation The vector equation of the plane is given as: \[ \vec{r} \cdot (-\hat{i} + \hat{j} + 2\hat{k}) = 9 \] This indicates that the normal vector to the plane is \(\vec{n} = -\hat{i} + \hat{j} + 2\hat{k}\). ...
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RD SHARMA-THE PLANE -Solved Examples And Exercises
  1. Find the vector equation of a plane passing through a point having ...

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  2. Find the Cartesian form of equation of a plane whose vector equation i...

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  3. Find the Cartesian form of equation of a plane whose vector equation i...

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  4. Find the vector equations of the coordinates planes.

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  5. Find the vector equation of each one of following plane: 2x-y+2z=8

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  6. Find the vector equation of each one of following plane: x+y-z=5

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  7. Find the vector equation of each one of following plane: x+y=3

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  8. Find the vector and Cartesian equations of a plane passing through the...

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  9. If vec n is a vector of magnitude sqrt(3) and is equally inclined wit...

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  10. The coordinate of the foot of the perpendicular drawn from  the origin...

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  11. Find the equation of the plane passing through the point (2,3,1) ha...

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  12. If the axes are rectangular and P is the point (2, 3, -1), find the eq...

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  13. Find the intercepts made on the coordinate axes by the plane 2x+y-2z=3...

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  14. Find the equation of the plane that bisects the line segment joining ...

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  15. Show that the normal to the following planes are perpendicular to each...

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  16. Show that the normal to the following planes are perpendicular to each...

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  17. Show that the equation of the planes are perpendicular to each other. ...

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  18. Show that the normal vector to the plane 2x+2y+2z=3 is equally incline...

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  19. Find a vector of magnitude 26 units normal to the plane 12 x-3y+4z=1.

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  20. Find the equation of the plane which bisects the line segment joining ...

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