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Find the equation of the plane which is ...

Find the equation of the plane which is perpendicular to the plane `5x+3y+6z+8=0` adn which contains the line of intersection of the planes `x+2y+3z-4=0a n d2x+y-z+5=0.`

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To find the equation of the plane that is perpendicular to the plane \(5x + 3y + 6z + 8 = 0\) and contains the line of intersection of the planes \(x + 2y + 3z - 4 = 0\) and \(2x + y - z + 5 = 0\), we can follow these steps: ### Step 1: Identify the normal vector of the given plane The normal vector of the plane \(5x + 3y + 6z + 8 = 0\) can be derived from the coefficients of \(x\), \(y\), and \(z\): \[ \text{Normal vector} = (5, 3, 6) \] ...
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RD SHARMA-THE PLANE -Solved Examples And Exercises
  1. Find the equation of the plane passing through the intersection of the...

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  2. Find the equation of the plane through the line of intersection of ve...

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  3. Find the equation of the plane which is perpendicular to the plane 5x+...

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  4. Find the equation of a plane through the intersection of the planes v...

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  5. Find the vector equation of the following planes in non-parametric f...

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  6. Find the vector equation of the plane vec r=(1+s-t) hat i+(2-s) hat ...

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  7. Find the Cartesian form the equation of the plane vec r=(s+t) hat i+...

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  8. Find the vector equation of the following plane in scalar product form...

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  9. The plane x-2y+3z=0 is rotated through a right angle about the line of...

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  10. The plane l x+m y=0 is rotated through an angle alpha about its line...

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  11. Find the vector equation of the line passing through the point (1,-1,2...

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  12. Find the vector equation of the plane passing through the intersection...

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  13. If 30 oxen can plough 1/7th of the field in 4 hrs , in how many hour w...

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  14. Find the equation of the plane through the points (1,0,-1),(3,2,2) and...

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  15. Find the angle between line (x+1)/3=(y-1)/2=(z-2)/4 and the plane 2x+y...

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  16. Show that the line whose vector equation is vec r=(2 hat i-2 hat j+3)...

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  17. Show that the line whose vector equation is vec r = dot(2 hat i+5 hat...

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  18. Find the vector equation of the line passing through the point (1,-1,2...

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  19. State when the line vec rdot vec a+lambda vec b is parallel to the pl...

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  20. Find the plane passing through (4,-1,2) and parallel to the lines (x+2...

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