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The plane through the point (-1,-1,-1) a...

The plane through the point (-1,-1,-1) and containing the of intersection of the planes `r*(hat(i)+3hat(j)-hat(k))=0andr*(hat(j)+2hat(k))=0` is

A

`r*(hat(i)+2hat(j)-3hat(k))=0`

B

`r*(hat(i)+4hat(j)+hat(k))=0`

C

`r*(hat(i)+5hat(j)-5hat(k))=0`

D

`r*(hat(i)+hat(j)+3hat(k))=0`

Text Solution

Verified by Experts

The correct Answer is:
A
The cartesian from of an equation of plane is
`x+3y-z=0`
`and" "y+2z=0`
The line intersection of two planes is
`(x+3y-z)+lamda(y+2z)=0`
Since, it is passing through `(-1,-1,-1)`.
`:." "(-1-3+1)+lamda(-1-2)=0`
`rArr" "-3-3lamda=0`
`rArr" "lamda=-1`
`:." "(x+3y-z)-1(y+2z)=0`
`rArr" "x+2y-3z=0`
Hence, equation of plane is
`r*(hat(i)+2hat(j)-3hat(k))=0`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PLANE-Practice exercise (Exercise 2) Miscellaneous problems
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  2. The image of the point (1,2,3) by the plane, x+y+z+3=0 is

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. A plane makes intercepts -6,3,4 upon the coordinate axes. Then, the le...

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  18. The equation of the plane through the line of intersection of the plan...

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  19. If the axes are rectangular and P is the point (2, 3, -1), find the eq...

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  20. The equation of a plane through the point (2, 3, 1) and (4, -5, 3) and...

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