The equation of the plane passing through the point 1,1,1) and
perpendicular to the planes `2x+y-2z=5a n d3x-6y-2z=7,`
is
`14 x+2y+15 z=3`
`14 x+2y-15 z=1`
`14 x+2y+15 z=31`
`14 x-2y+15 z=27`
A
`14x+2y+15x=31`
B
`14x+2y-15z=1`
C
`14x+2y+15x=3`
D
`14x-2y+15z=27`
Text Solution
Verified by Experts
The correct Answer is:
A
(a) given that required plane is perpendicular to the given two planes , therefore , the ormal vector of required plane I sperpendicular to the normal to the given planes . therefore , the normal vector of required plane is parallel to the vector : `|{:(hati,hatj,hatk),(2,1,-2),(3,-6,-2):}|=-14hati-2hatj-15hatk` thus , the equation of required of required plane passing through (1,1,1) will be : `-14(x-1)-2(y-1)-15(z-1)=0` `implies 14x+2y+15z=31`
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