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If the distance between the planes 8x+12...

If the distance between the planes `8x+12y-14z=2 and 4x+6y-7z=2` can be expressed in the form `(1)/(sqrt(N))`, where N is natural, then the value of `(N(N+1))/(2)` is

A

`4950`

B

`5050`

C

`5150`

D

`5151`

Text Solution

Verified by Experts

The correct Answer is:
(d)
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Find the distance between the planes 2x+3y+4z=4 and 4+6y+8z=12 .

Find the distance between the planes x+2y+3z+7=0 and 2x+4y+6z+7=0 .

Find the angle between the plane: 2x-y+z=4\ a n d\ x+y+2z=3

Find the angle between the plane: 2x-3y+4z=1\ a n d-x+y=4.

Find the angle between the plane: x-y+z=5\ a n d\ x+2y+z=9

Find the angle between the plane: x+y-2z=3\ a n d\ 2x-2y+z=5 .

Distance between the two planes: 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12 is

The shortest distance between the line 1+x=2y=-12z and x=y+2=6z-6 is

ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
  1. Consider three vectors p=i+j+k, q=2i+4j-k and r=i+j+3k. If p, q and r ...

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  2. Intercept made by the circle zbarz+bara+a barz+r=0 on the real axis ...

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  3. If the distance between the planes 8x+12y-14z=2 and 4x+6y-7z=2 can be ...

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  4. A plane passes through thee points P(4, 0, 0) and Q(0, 0, 4) and is pa...

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  5. If from the point P(f, g, h) perpendicular PL and PM be drawn to yz an...

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  6. The plane XOZ divides the join of (1, -1, 5) and (2, 3, 4)in the ratio...

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  7. A variable plane forms a tetrahedron of constant volume 64k^3 with the...

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  8. Let ABCD be a tetrahedron such that the edges AB, AC and AD are mutual...

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  9. Equations of the line which passe through the point with position vect...

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  10. Which of the following planes are parallel but not identical? P1: 4x...

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  11. A parallelopied is formed by planes drawn through the points (1, 2, 3)...

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  12. Vector equation of the plane r = hati-hatj+ lamda(hati +hatj+hatk)+mu(...

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  13. The vector equations of two lines L1 and L2 are respectively, L1:r=2i+...

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  14. Consider the plane (x,y,z)= (0,1,1) + lamda(1,-1,1)+mu(2,-1,0) The dis...

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  15. The value of a for which the lines (x-2)/(1)=(y-9)/(2)=(z-13)/(3) and ...

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  16. For the line (x-1)/(1)=(y-2)/(2)=(z-3)/(3), which one of the following...

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  17. Given planes P1:cy+bz=x P2:az+cx=y P3:bx+ay=z P1, P2 and P3 pass...

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  18. The lines (x-2)/(1)=(y-3)/(1)=(z-4)/(-k) and (x-1)/(k)=(y-4)/(2)=(z-5)...

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  19. The line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the curve xy=c^2, z...

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  20. The line which contains all points (x, y, z) which are of the form (x,...

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