Consider a plane

x+y-z=1 and the point A(1,2,-3)

A line L has the equation

x=1+3r

y=2-r

z=3+4r

Equation of the plane containing the line L and the point A has the equation

(A) x-3y+5

(B)x+3y-7=0

(C) 3x-y-1=0

(D)3x+y-5=0

Put any 2 values of r to get the coordinates of any 2 points that lie on the linegiven by
x=1+3r
y=2-r
z=3+4r
Let those points be B and C
So, we need to the eqn of a plane which contains 3 points A, B and C.
Use the condition of coplanarity of 3 points to find the eqn of the plane using the triple product as


Answer is option B