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

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`x+y=3` This is in Cartesian form, to convert this to vector form, this can be done as shown below:
`(x \hat{\i}+y \hat{\j}+z \hat{k}) \cdot(\hat{\i}+\hat{\j})=3`
We know `x \hat{\i}+y \hat{\j}+\rm{z} \hat{\rm{k}}= {\rm{r}}`
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RD SHARMA-THE PLANE -Solved Examples And Exercises
  1. Find the vector equation of each one of following plane: 2x-y+2z=8

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. Find the vector and the Cartesian equation of the plane which pases th...

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  18. If O be the origin and the coordinates of P be(1," "2," "" "3) , th...

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  19. Find the vector equation of a plane at a distance of 5 units from the ...

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  20. Reduce the equation of the plane x-2y-2z=12 to normal form and hence f...

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