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Find the vector equation of the line passing through `(1,2,3)` and parallel to the planes `vecr .(hati-hatj+2 hatk)=5` and `vecr .(3 hati+hatj+hatk)=6`

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Find the vector equation of the line passing through (1,2,3) and perpendicular to the plane vecr.(hati+2hatj-5hatk)+9=0

Find the eqation of the plane passing through (a,b,c) and parallel to the plane vecr.(hati+hatj+hatk)=2

Find the equation of the plane passing through the line of intersection of the planes vecr .(hati+hatj+hatk)=1 and vecr.(2 hati+3 hatj-hatk)+4=0 and parallel to x -axis.

Find the vector equation of the plane passing through the intersection of the palnes vecr.(2hati+2hatj-hat3k) = 7, vecr.(2hati+5hatj+3hatk) = 9 and through the point (2, 1, 3)

Find the vector equation of the plane passing through the intersection of the planes barr.(hati+hatj+hatk)=6 and barr.(2hati+3hatj+4hatk)=-5 at the point (1,1,1) .

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

Find the equation of the plane which contains the line of intersection of the planes vecr .(hati+2 hatj+3 hatk)-4 =0 , vecr .(2 hati+hatj-hatk)+5=0 and which is perpendicular to the plane vecr .(5 hati+3 hatj-6 hatk)+8=0

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V PUBLICATION-THREE DIMENSIONAL GEOMETRY-QUESTION BANK
  1. Find the equation of the plane which contains the line of intersectio...

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  2. Find the distance of the point (-1,-5,-10) from the point of intersecț...

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  3. Find the vector equation of the line passing through (1,2,3) and paral...

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  4. Find the vector equation of the line passing through the point (1,2,-4...

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  5. Prove that if a plane has the intercepts a, b, c and it is at a distan...

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  6. Distance between the two planes: '2 x+3 y+4 z=4' and '4 x+6 y+8 z=(12)...

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  7. The planes '2 x-y+4 z=5' and '5 x-2.5 y+10 z=6' are

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  8. Can a line have direction angles 45^circ, 60^circ, 135^circ?

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  9. A line makes angles of 45^circ and 60^circ with the positive axes of X...

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  10. Find the direction cosine of a line which makes equal angles with the...

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  11. 1, '-2,-2' are direction ratios of a line. What are its direction cosi...

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  12. Find d.c.'s of the line passing through the points 'P(4,3,-5)' and 'Q(...

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  13. A line passes through the points (6,-7,-1) and (2,-3,1) Find the direc...

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  14. Find the angle between the lines whose diréction ratios are '2,3,4' an...

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  15. Find the obtuse angle between the lines with direction ratios '3,-6,2'...

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  16. If points 'P, Q' are '(2,3,-6)' and '(3,-4,5)', find the angle that OP...

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  17. If A, B, C, D are the points (3,4,5),(4,6,3),(-1,2,4) and (1,0,5), fin...

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  18. Find the coordinates of foot of perpendicular drawn from the point (1,...

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  19. Prove that the Iine joining the midpoints of the two sides of a triang...

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  20. The cartesian equations of a line are 6 x-2=3 y+1=2 z-2. Find directi...

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