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Distance between the two planes: 2x + 3y...

Distance between the two planes: `2x + 3y + 4z = 4`and `4x + 6y + 8z = 12`is(A) 2 units (B) 4 units (C) 8 units (D) `2/(sqrt(29))`units

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Verified by Experts

The given equation of planes are known
thus, distance between them is
`D=|(d_2-d_1)/sqrt(a^2+b^2+c^2)|`
thus
`D=|(6-4)/sqrt(2^2+3^2+4^2)|`
`D=2/sqrt29`
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NCERT-THREE DIMENSIONAL GEOMETRY-MISCELLANEOUS EXERCISE
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  2. Find the equation of the plane which contains the line of intersectio...

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  3. If O be the origin and the coordinates of P be(1, 2, -3), then find ...

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  4. Find the coordinates of the point where the line through (5, 1, 6) an...

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  5. Find the coordinates of the point where the line through (5, 1, 6) an...

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  6. Find the equation of the plane passing through the point ( 1, 3, 2)an...

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  7. Find the coordinates of the point where the line through (3, 4, 5)a...

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  8. The planes: 2x y + 4z = 5 a n d 5x 2. 5 y + 10 z = 6are(A) Perpendic...

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  9. Find the equation of the plane passing through (a, b, c) and parallel...

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  10. Find the shortest distance between lines vecr=6 hat i+2 hat j+ hat k...

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  11. If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/2and (x-1)/(3k)=(y-1)/1=(z-6...

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

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  13. Find the equation of a line parallel to x-axis and passing through th...

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  14. If the coordinates of the points A, B, C, D be (1, 2, 3), (4, 5, 7),...

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  15. If l1,m1,n1and l2,m2,n2are the direction cosines of two mutually per...

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  16. Find the angle between the lines whose direction ratios are a, b, c a...

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  17. Show that the line joining the origin to the point (2, 1, 1)is perpen...

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

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  19. Prove that if a plane has the intercepts a, b, c and is at a distance...

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

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