The equation of plane passing through a point A(2, -1, 3) and parallel to the vectors a = (3, 0, -1) and b = (-3, 2, 2) is

Options

A. `2x-3y+6z-25=0`
B. `2x-3y+6z+25=0`
C. `3x-2y+6z-25=0`
D. `3x-2y+6z+25=0`

Answer

A

Explanation

The equation of any plane through `(2,-1,3)` is
`a(x-2)+b(y+1)+c(z-3)=0`
Since, Eq. (i) is parallel to a and b
`:." "3a+0b-c=0`
and `-3a+2b+2c=0`
`implies" "(a)/(2)=(b)/(3-6)=(c)/(6)=k`
`implies" "a=2k,b=-3k,c=6k`
On putting the values of a, b and c in Eq. (i), we get
`2k(x-2)-3k(y+1)+6k(z-3)=0`
`implies" "2x-3y+6z-25=0`