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Consider the planes 3x-6y+2z+5=0a n d4x-...

Consider the planes `3x-6y+2z+5=0a n d4x-12+3z=3.` The plane `67 x-162 y+47 z+44=0` bisects the angel between the given planes which a. contains origin b. is acute c. is obtuse d. none of these

A

contains origin

B

is acute

C

is obtuse

D

none of these

Text Solution

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The correct Answer is:
a, b
`" "3x-6y+2z+5=0" "`(i)
`" "-4x+12y-3z+3=0" "` (ii)
Bisectors are `(3x-6y+2z+5)/(sqrt(9+36+4)) = pm (-4x+ 12y-3z+ 3)/(sqrt(16+144+ 9))`
The plane which bisects the angle between the plants that contains the origin.
`" "13(3x-6y+2z+5)=7(-4x+12y-3z+3)`
`" "67x-162y+47z+44=0" "` (iii)
Further, `3xx(-4)+ (-6)(12)+ 2xx(-3) lt 0`
Hence, the origin lies in the acute angle.
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Multiple)
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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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  17. The equation of the line x+y+z-1=0, 4x+y-2z+2=0 written in the symmetr...

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