about to only mathematics

Options

A. `x+2y-2z=0`
B. `3x+2y-2z=0`
C. `x-2y+z=0`
D. `5x+2y-4z=0`

Answer

C

Explanation

The DR's of normal to the plane containing `(x)/(3)=(y)/(4)=(z)/(2)` and `(x)/(4)=(y)/(z)=(z)/(3).`
`n_(1)=|{:(hati,hatj,hatk),(3,4,2),(4,2,3):}|=(8hati-hatj-10hatk)`

Also, equation of plane containing `(x)/(2)=(y)/(3)=(z)/(4)` and DR's of normal to be `n_(1)=ahati+bhatj+chatk`
`implies" "ax+by+cz=0" "...(i)`
where `n_(1):n_(2)=0`
`implies" "8a-b-10c=0" "...(ii)`
and `n_(2)_|_(2hati+3hatj+4hatk)`
`implies" "2a+3b+4c=0" "...(iii)`
From Eqs (ii) and (iii),
`(a)/(-4+30)=(b)/(-20-32)=(c)/(24+2)`
`implies" "(a)/(26)=(b)/(-52)=(c)/(26)`
`implies" "(a)/(1)=(b)/(-2)=(c)/(a)" "...(iv)`
From Eqs. (i) and (iv), required equation of plane is
`x-2y+z=0`