Find ten equation of the plane passing through the point `(0,7,-7)` and containing the line `(x+1)/(-3)=(y-3)/2=(z+2)/1` .

Options

A. x+y+z=1
B. x+y+z=2
C. x+y+z=0
D. None of these

Answer

C

Explanation

The equation of plane containing the line
`(x+1)/(-3)=(y-3)/(2)=(z+2)/(1)` is
`a(x+1)+b(y-3)+c(z+2)=0` . . . (i)
also, `-3a+2b+c=0` . . (ii)
Also, plane passes through
(0,7,-7).
`thereforea+4b-5c=0` . . . (iii)
From eqs. (ii) and (iii),
`(a)/(-14)=(b)/(-14)=(c)/(-14)`
`implies(a)/(1)=(b)/(1)=(c)/(1)`
substituting the value of a,b,c in Eq. (i), we get
x+y+z=0