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The equations of the plane which pass...

The equations of the plane which passes through `(0,0,0)` and which is equally inclined to the planes `x-y+z-3=0a n dx+y=z+4=0` is/are a. `y=0` b. `x=0` c. `x+y=0` d. `x+z=0`

A

`y=0`

B

`x=0`

C

`x+y=0`

D

`x+z=0`

Text Solution

Verified by Experts

The correct Answer is:
a, c
The required plane is parallel to the bisector of the given planes.
Bisector are `(x-y+z-3)/(sqrt3)= pm (x+y+z+4)/(sqrt3)`
or `2y+7 =0 and 2x+2y+1=0`. Hence, the planes are `y=0 and x+y=0`.
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Multiple)
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  3. If the planes vecr.(hati+hatj+hatk)=q(1),vecr.(hati+2ahatj+hatk)=q(2)a...

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  4. A line with direction cosines proportional to 1,-5, a n d-2 meets l...

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  5. Let P=0 be the equation of a plane passing through the line of inte...

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  6. The equation of the line x+y+z-1=0, 4x+y-2z+2=0 written in the symmetr...

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  7. Consider the planes 3x-6y+2z+5=0a n d4x-12+3z=3. The plane 67 x-162 y+...

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  8. If the lines (x-2)/(1)=(y-3)/(1)=(z-4)/(lamda) and (x-1)/(lamda)=(y-4)...

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  9. The equations of the plane which passes through (0,0,0) and which i...

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  10. The x-y plane is rotated about its line of intersection with the y-...

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  11. The equation of the plane which is equally inclined to the lines (x...

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  12. Which of the following lines lie on the plane x+2y-z+4=0? a. (x-1)...

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  13. If the volume of tetrahedron A B C D is 1 cubic units, where A(0,1,...

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  14. A rod of length 2 units whose one ends is (1, 0, -1) and other end to...

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  15. Consider a set of point R in which is at a distance of 2 units from t...

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  16. The equation of the line throgh the point veca parallel to the plane v...

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  17. The equation of the line x+y+z-1=0, 4x+y-2z+2=0 written in the symmetr...

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