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The three planes 4y+6z=5,2x+3y+5z=5a n d...

The three planes `4y+6z=5,2x+3y+5z=5a n d6x+5y+9z=10` a. `` meet in a point b. have a line in common c. form a triangular prism d. none of these

A

meet in a point

B

have a line in common

C

form a triangular prism

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
b
Plane pasing through the line of intersection of planes `4y+6z= 5 and 2x+3y + 5z= 5 ` is
`" "(4y+6z-5)+ lamda(2x+3y+5z-5)=0`
or `" "2lamdax+(3lamda+4)y + (5lamda+6)z- 5lamda-5=0`
Clearly, for `lamda= -3`, we get the plane `6x+5y+9z=10 `.
Hence, the given three planes have common line of intersection.
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
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  2. The line through of the plane passing through the lines (x-4)/(1)=(y-3...

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  3. The three planes 4y+6z=5,2x+3y+5z=5a n d6x+5y+9z=10 a. meet in a poi...

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

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  5. Equation of the pane passing through the points (2,2,1)a n d(9,3,6)...

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  6. Value of lamda such that the line (x-1)/(2)=(y-1)/(3)=(z-1)/(lamda) is...

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  7. The equation of the plane passing through the intersection of x + 2y +...

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  8. The plane 4x+7y+4z+81=0 is rotated through a right angle about its ...

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  9. The vector equation of the plane passing through the origin and the li...

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  10. The two lines vecr=veca+veclamda(vecbxxvecc) and vecr=vecb+mu(veccxxve...

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  11. The projection of the line (x+1)/(-1)=y/2=(z-1)/3 on the plane x-2y+z=...

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  12. The direction cosines of a line satisfy the relations lambda(l+m)=n ...

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  13. The intercepts made on the axes by the plane the which bisects the ...

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  14. Find the angle between the lines whose direction cosines are given by ...

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  16. A plane passes through a fixed point (a ,b ,c)dot The locus of the ...

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  17. What is the nature of the intersection of the set of planes x+a y+(...

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  18. Find the equation of a straight line in the plane vecr.vecn=d which is...

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  19. What is the equation of the plane which passes through the z-axis and ...

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