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Find the vector and Cartesian equation of the plane that passes through the point (1,4,6) and the normal vector to the plane is `hati-2hatj+hatk`.

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The correct Answer is:
`vecr.(-hati+2hatj-hatk)=1, x-2y+z=1=0`
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Find the vector and cartesian equations of the plane that passes through the point (0, 1, -2) and normal to the vector hati + hatj + hatk .

Find the vector and cartesian equation of the line passing through the point P (1,2,3) and parallel to the planes : vec(r).(hati - hatj + 2 hatk) = 5. vec(r).(3hati + hatj + hatk) = 6.

Find the vector and Cartesian equations of the plane passing through the point (1,2,-4) and parallel to the lines vecr=(hati+2hatj+hatk)-lambda(2hati+3hatj+6hatk) and vecr=(hati-3hatj+5hatk)+mu(hati+hatj-hatk) .

Find the vector and cartesian equation of plane which passes through the point (1,3,-2) and normal to the vector (2hati+hatj-2hatk) .

Find the vector and cartesian equation of the plane : (i) that passes through the point (5,2,-4) and perpendicular to the line with direction-ratios lt 2, 3, -1 gt (ii) that passes through the point (1,0, -2) and the normal to the plane is hati + hatj - hatk (iii) that passes through the point (1,4,6) and the normal vector to the plane is hati - 2 hatj + hatk .

RS AGGARWAL-THE PLANE-Exercise 28B
  1. Find the vector equation of the plane which is at a distance of 6/sqrt...

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  2. Find the vector and Cartesian equations of a plane which is at a dista...

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  3. Find the vector and Cartesian equation of the plane that passes throug...

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  4. Find the length of perpendicular from the origin to the plane vecr.(3h...

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  5. Find the Cartesian equation of the plane whose vector equation is vecr...

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  6. Find the vector equation of a plane whose Cartesian equation is 5x-7y+...

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  7. Find a unit vector normal to the plane is x-2y+2z=6.

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  8. Find the direction cosines of the normal to the plane is (3x-6y+2z=7.

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  9. For each of the following planes, find the direction cosines of the no...

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  10. Find the vector and Cartesian equations of the plane passing throgh th...

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  11. Find the coordinates of the foot of the perpendicular drawn from the o...

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  12. Find the co-ordinates of the foot of perpendicular and the length of p...

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  13. Find the length of the foot of the perpendicular from the point (1,1,2...

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  14. From the point P(1,2,4) a perpendicular is drawn on the plane 2x+y-2z+...

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  15. Find the coordinates of the foot of the perpendicular and the perpendi...

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  16. Find the coordinates of the image of the point P(1, 3, 4) in the plane...

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  17. Find the point where the line (x-1)/2=(y-2)/-3=(z+3)/4 meets the plane...

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  18. find the coordinates of point where the line through (3,-4,-5) and (2,...

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  19. Find the distance of the point (2,3,4) from the plane 3x+2y+2z+5=0 mea...

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  20. Find the distance of the point (0,-3,2) from the plane 3x+2y+2z+5=0, ...

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