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Find the cartesian equation of the follo...

Find the cartesian equation of the following planes.
`vecr.(hati+hatj-hatk)=2`

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Find the Cartesian equation of the following plane: vecr cdot [(s-2t)hati + (3-t)hatj + (2s+t)hatk] = 15

Find cartesian equations of the plane containing the lines: vecr=2hati+hatj-3hatk+lambda(hati+2hatj+5hatk) and vecr=3hati+3hatj-7hatk+mu(3hati-2hatj+5hatk)

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PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Fill ups The equation of the plane containing the points (2,0,0),(0,3,...

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  2. Fill ups A plane 'p' passes through the point P(1,-2,3). If O is the o...

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  3. Find the cartesian equation of the following planes. vecr.(hati+hatj-h...

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  4. If a line makes an angle of (pi)/(4) each of y and z axis, then the an...

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  5. Fill ups The equation of the plane containing the points (2,0,0),(0,3,...

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  6. Fill ups Distance of the point (4,-2,3) from Y-axis is……………… .

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  7. Fill ups Intercepts made by the plane 2x-3y+5z-30=0 on the coordinate ...

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  8. The acute angle between the planes vecr.(2hati-3hatj+hatk)=1 and vecr....

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  9. Fill ups The image of the poidnt (1,-2,3) in the plane x-2y+3z-14=0 is...

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  10. Fill ups The image of the poidnt (1,-2,3) in the plane x-2y+3z-14=0 is...

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  11. True or false The points (a,0,0),(0,b,0) and (0,0,c) are collinear (ab...

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  12. The points (1, 2, 3), (-2, 3, 4) and (7,0,1) are collinear.

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  13. The unit vector normal to the plane x+2y+3z-6=0 is (1)/(sqrt14)hati+(2...

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  14. True or false The line x=y=z lies in the plane x-2y+z-1=0.

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  15. True or false The line vecr=2hati-3hatj+hatk+t(hati-hatj+2hatk) lies i...

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  16. True or false The projection of the point (alpha,beta,gamma) on the XO...

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  17. The intercepts made by the plane 2 x – 3 y + 5z+4 = 0 on the co-ordina...

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  18. True or false The projection of the point (alpha,beta,gamma) on the z-...

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  19. True or false The vector equation of the line (x-5)/3=(y+4)/7=(z-6)/2 ...

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  20. The acute angle between the planes vecr.(2hati-3hatj+hatk)=1 and vecr....

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