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The planes 2x - y + 4z = 5 and 5x - 2....

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

A

perpendicular

B

parallel

C

intersect y-axis

D

passes through `(0,0,5/4)`

Text Solution

Verified by Experts

The correct Answer is:
B
Direction of the given planes are `(2,-1,4)` and `(5,-2.5,10)`
`:. 2/5 = (-1)/(-2.5) = (4)/(10) rArr (4)/(10) = 4/10 = 4/10`
Therefore, `(a_(1))/(a_(2)) = (b_(1))/(b_(2)) = (c_(1))/(c_(2))`
So, the given planes are parallel.
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NAGEEN PRAKASHAN ENGLISH-THREE-DIMENSIONAL GEOMETRY -Miscellaneous Exercise
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  2. If the coordinates of the points A ,B ,C ,D are (1,2,3),(4,5,7),(-4,3,...

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

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

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  5. Write the vector equation of the plane, passing through the point (a ,...

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  6. Find the shortest distance between lines vecr = 6hati+2hatj+2hatk+lam...

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  7. Find the coordinate of the point where the line through (5, 1, 6) and ...

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

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  9. Find the coordinates of the point where the line through (3, -4, -5...

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  10. Find the equation of the plane passing through the point (-1, 3, 2)...

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  11. If the points (1," "1," "p)" "a n d" "(" "3," "0," "1) be equidistant ...

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  12. Find the equation of the plane passing through the line of intersectio...

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  13. If O be the origin and the coordinates of P be(1," "2," "" "3) , th...

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  14. Find the equation of the plane which contains the line of intersection...

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  15. Find the distance of the point (-1,-5,-10) from the point of the inter...

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  16. Find the vector equation o the line passing through (1,2,3) and parall...

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

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  18. Prove that if a plane has the intercepts a ,\ b ,\ c\ a n d\ is at a ...

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

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

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