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Find a normal vector to the plane 2x-y+2...

Find a normal vector to the plane `2x-y+2z=5.` Also, find a unit vector normal to the plane.

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To find a normal vector to the plane given by the equation \(2x - y + 2z = 5\), we can follow these steps: ### Step 1: Identify the coefficients from the plane equation The general form of a plane equation is given by: \[ Ax + By + Cz = D \] where \(A\), \(B\), and \(C\) are the coefficients of \(x\), \(y\), and \(z\) respectively. From the equation \(2x - y + 2z = 5\), we can identify: ...
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RD SHARMA-THE PLANE -Solved Examples And Exercises
  1. Find the equation in Cartesian form of the plane passing through the ...

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  2. Find the vector equation of the plane whose Cartesian form of equals 3...

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  3. Find a normal vector to the plane 2x-y+2z=5. Also, find a unit vector ...

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  4. Find the angle between the normal to the planes 2x-y+z=6\ a n d\ x+y+2...

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  5. Find the angles at which the normal vector to the plane 4x+8y+z=5 is i...

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  6. Find the vector equation of a plane passing through a point having ...

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

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

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  9. Find the vector equations of the coordinates planes.

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

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

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

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

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

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

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

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

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

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

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

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