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 angle between the given planes which a. contains origin b. is acute c. is obtuse d. none of these

Options

A. contains origin
B. is acute
C. is obtuse
D. none of these

Answer

a, b

Explanation

`" "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.