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If the planes 2x+y-2z=0and x+2y+kz=0 are...

If the planes `2x+y-2z=0and x+2y+kz=0` are at right angles, then the value of k is

A

2

B

`-2`

C

`(1)/(2)`

D

`-(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given two planes are
`2x+y-2z=0`
`and" "x+2y+kz=0`
Since these two planes are perpendicular , then
`a_(1)a_(2)+b_(1)b_(2)+c_(1)c_(2)=0`
`rArr" "2*1+1*2-2(k)=0`
`rArr" "-2k+4=0`
`rArr" "k=2`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PLANE-Practice exercise (Exercise 2) Miscellaneous problems
  1. Find the angle between the planes vec rdot(2 hat i- hat j+ hat k)=6a ...

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  2. The distance of the point (2,1,0) from the plane 2x+y+2z+5=0

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  3. If the planes 2x+y-2z=0and x+2y+kz=0 are at right angles, then the val...

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  4. The plane 2x+3y+4z=1 meets the coordinate axis in A, B, C. The centroi...

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  5. Equation of the plane parallel to the planes x+2y+3z-5=0," "x+2y+...

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  6. The image of the point (1,2,3) by the plane, x+y+z+3=0 is

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  7. The plane through the point (-1,-1,-1) and containing the of intersect...

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  8. the equation of a plane through the line of intersection the planes x+...

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  9. The equation of the plane perpendicular to the line (x-1)/1=(y-2)/(-1)...

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  10. The equation of the plane which makes with coordinate axes, a triangle...

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  11. The equation of the plane containing the line 2x-5y""+""z""=""3;""x"...

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  12. The angle between r=(1+2mu)hat(i)+(2+mu)hat(j)+(2mu-1)hat(k) and the p...

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  13. An equation of a plane parallel to the plane x-2y +2 z-5=0 and at a un...

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  14. If the angle between the line x(y-1)/2=(z-3)/lamda and the plane x+2y...

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  15. Let the line (x-2)/3=(y-1)/(-5)=(z+2)/2 lie in the plane x+3y-alphaz+b...

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  16. A variable plane x/a+y/b+z/c=1 at a unit distance from origin cuts the...

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  17. A variable plane moves so that the sum of the reciprocals of its inter...

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  18. Let L be the line of intersection of the planes 2x""+""3y""+""z""="...

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  19. The equation of the plane passing through the line of intersection of ...

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  20. Foot of perpendicular drawn from the origin to the plane 2x-3y+4z=29 i...

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