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Let the line (x-2)/3=(y-1)/(-5)=(z+2)/2 ...

Let the line `(x-2)/3=(y-1)/(-5)=(z+2)/2` lie in the plane `x+3y-alphaz+beta=0. Then (alpha,beta) equals

A

(6,-17)

B

(-6,7)

C

(5,-15)

D

(-5,15)

Text Solution

Verified by Experts

The correct Answer is:
B
Direction ratios of given line are (3,-5,2).
Dierection ratios of normal to the plane are `(1,3,-alpha)`
Since, line is perpendicular to the normal.
`:.3(1)-5(3)+2(-alpha)=0rArr3-15-2alpha=0`
`rArr" "2alpha=-12rArralpha=-6`
Also, point (2,1-2) lies on the given plane.
`2+3+6(-2)+beta=0rArr=0rArrbeta=7`
`rArr" "(alpha,beta)=(-6,7)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PLANE-Practice exercise (Exercise 2) Miscellaneous problems
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  2. If the angle between the line x(y-1)/2=(z-3)/lamda and the plane x+2y...

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

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

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

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

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

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

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

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

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

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

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  13. Find the vector equation of the plane passing through the intersectio...

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  14. Find the vector equation of the plane passing thrugh the points (2,5,-...

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  15. Find the equation of the plane which bisects the line segment joining ...

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  16. The equation of the plane through the intersection of the planes x+y+...

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  17. Find the equation of the plane passing through the line intersection o...

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  18. The image of the point with position vector hat(i)+3hat(k) in the plan...

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  19. The equation of the plane through the point (2,5,-3) and perpendicular...

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  20. The equation of the plane passing through the intersection of the plan...

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