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Consider the plane 10x - 5y + 4z = 20, f...

Consider the plane `10x - 5y + 4z = 20`, find the point which is closest to origin and also find the direction cosines of the normal to plane.

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The correct Answer is:
`(200/141,- 100/141, 80/141), (10/sqrt(141), -5/sqrt(141), 4/sqrt(141))`
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AAKASH INSTITUTE-THREE DIMENSIONAL GEOMETRY -TRY YOURSELF
  1. Find the distance of the plane 2x - 3y + 4z = 6 from the origin.

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  2. Find the foot of perpendicular drawn from the point P(0, 0, 0) to the ...

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  3. Consider the plane 10x - 5y + 4z = 20, find the point which is closest...

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  4. Find the equation ot the plane through the point p(5, 3, -1) perpendic...

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  5. Find the equation of the plane through the point (0, 1, 2) and parpend...

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  6. Find the equation of a plane passing through origin and which is perpe...

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  7. Find the equation of the plane passing through the points (1,-1,2)a n ...

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  8. Find the equation of the plane through the points A(3, 2, 0), B(1, 3, ...

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  9. Find equation of the plane through (2, 1, 4), (1, -1, 2) and (4, -1, 1...

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  10. Find the equation of the plane containing the points P(2, 3, -1), Q(6,...

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  11. A plane meets the coordinates axis in A, B, C such that the centroid o...

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  12. A variable plane is at a constant distance p from the origin and meets...

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  13. Find the vector equation of a plane containing line of intersection of...

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  14. Find the equation of the plane through the line of intersection of the...

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  15. Find an equation for the plane through P(0)=(1, 0, 1) and passing thro...

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  16. Find the equation of a plane containing the line of intersection of...

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  17. Show that lines (x-2)/5=(y+1)/1=(z-2)/-6 and (x+3)/-8=(y-2)/-1=(z-8)/7...

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  18. Find x such that the four points A\ (3,\ 2,\ 1), B(4, x ,\ 5), C\ (4,...

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  19. Find the angle between the planes 2x + y - 2z = 5 and 3x - 6y - 2z = 7...

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  20. Find the angle between the planes 2x - y + 3z = 6 and x + y +2z =7.

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