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Find the cartesian form of the equation ...

Find the cartesian form of the equation of the plane.
`barr = (hati + hatj) + s(hati - hatj + 2hatk) + t(hati + 2hatj +hatk)`.

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`5x -y -3z = 4`
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Find the vector equation of the plane passing through the point hati + hatj -2hatk and hati + 2hatj + hatk, 2hati - hatj + hatk.

Find the Cartesian equation of the following planes : a. vec(r). (hati + hatj - hatk ) = 2 b. vec(r). (2 hati + 3 hatj - 4 hatk ) = 1 (c ) vec(r). [ (s - 2t) hati + (3 - t ) hatj + (2 s + t ) hatk] = 15

Find the angle between the line barr = (hati + 2hatj + hatk) + lambda(hati +hatj + hatk) and the plane barr*(2hati - hatj + hatk) = 5 .

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Find the vector and cartesian equations of the plane containing the lines : vec(r) = hati + 2 hatj - 4 hatk + lambda (2 hati + 3 hatj + 6 hatk) and vec(r) = 3 hati + 3 hatj - 5 hatk + mu (-2 hatj + 3 hatj + 8 hatk) .

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NAVNEET PUBLICATION - MAHARASHTRA BOARD-PLANE -Example for Practice
  1. Find the vector equation of the plane passing through the point A(1, 0...

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  2. Find the vector equation of the plane passing through the point hati +...

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  3. Line barr = (hati - hatj + hatk) + lambda(2hati- hatj + hatk) containe...

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  4. Find the equations of the planes parallel to the plane x - 2y + 2z -4 ...

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  5. If from a point P(a ,b ,c) perpendiculars P Aa n dP B are drawn to Y Z...

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  6. Find the cartesian form of the equation of the plane. barr = (hati ...

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

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  8. Find the equation of the plane passing through the intersection of the...

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  9. Prove that the lines (x-2)/1=(y-4)/4=(z-6)/7 and (x+1)/3=(y+3)/5=(z+5)...

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  10. A variable plane which remains at a constant distance 3p from the orig...

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  11. Find the angle between the planes whose vector equations are barr ...

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  12. If the line barr = (hati - 2hatj + 3hatk) + lambda(2hati + hatj + 2hat...

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  13. The planes barr *(3hati - 2hatj + phatk) =1 and barr *(-2hati + phatj ...

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  14. Find the value of p, if the planes barr *(phati - hatj + 2hatk) + 3 = ...

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  15. Find the angle between the line barr = (hati + 2hatj + hatk) + lambda(...

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  16. Find the angle between the line (x+1)/2=y/3=(z-3)/6and the plane 10 ...

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  17. Find the distance of the point 2hati + hatj + hatk) from the plane bar...

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  18. Find the distance of the point (1, 2-1) from the plane x -2y + 4z - 10...

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  19. Show that the points (1, 1, 1) and (-3, 0, 1) are equidistant from the...

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  20. Show that the points (1,-1,3) and (3, 4, 3) are equidistant from the p...

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