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Find the vector equation of the plane pa...

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

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The correct Answer is:
`vecr.(20hati+23hatj+26hatk)=69`
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Find the vector equation of the plane passing through the intersection of the planes vecr * ( hati + hatj + hatk ) =6 and vecr * ( 2 hati + 3 hatj + hatk )=-5 and the point ( 1,1,1) .

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

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

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

Find the equation of the plane passing through the line of intersection of the planes vecr.(hati+3hatj-hatk)=0 and vecr.(hatj+2hatk)=0 and also passing through the point 2hati+hatj-hatk .

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

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 cartesian equation of the plane| through the intersection of the planes vecr.(2hati+6hatj)+12=0 and vecr.(3hati-hatj+4hatk)=0 which are at a unit distance from the origin.

Find the equation of the plane passing through the point (3, 4, -1) and parallel to the plane vecr.(2hati-3hatj+5hatk)+2=0

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

KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-TEXTBOOK IILUSTRATIONS FOR PARCTICE WORK
  1. Find the shortest distance between the lines l1 and l2 whose vector eq...

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  2. Find the distance between the lines l1 and l2 given by vecr=hati+2hatj...

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  3. Find the vector equation of the plane which is at a distance of (6)/(s...

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  4. Find the direction cosines of the unit vector perpendicular to the pla...

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  5. Find the distance of the plane 2x – 3y + 4z - 6 = 0 from the origin.

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

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  7. Find the vector and cartesian equations of the plane which passes thro...

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  8. Find the vector equations of the plane passing through the points R(2,...

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  9. Find the equation of the plane with intercepts 2, 3 and 4 on the x, y ...

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

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  11. Show that the lines (x+3)/(-3)=(y-1)/(1)=(z-5)/(5) and (x+1)/(-1)=(y-2...

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  12. Find the angle between the two planes 2x + y - 2z = 5 and 3x – 6y – 2z...

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  13. Find the angle between the two planes 3x – 6y + 2z = 7 and 2x + 2y – 2...

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  14. Find the distance of a point (2, 5, -3) from the plane vecr.(6hati-3ha...

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

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  16. A line makes the angle alpha, beta , gamma and delta with the diagonal...

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  17. Find the equation of the plane that contains the point (1,-1, 2) and i...

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  18. Find the distance between the point P (6,5, 9) and the plane determine...

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  19. Show that the lines (x-a+d)/(alpha- delta)=(y-a)/(alpha)=(z-a-d)/(alph...

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  20. Find the coordinates of the point where the line through the points A ...

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