Question

Does there pass a plane through the lines x+4/3 =
y/2 =
z−1/3
and x/2 =
y−1/1 =
z+1/1
?
Justify.

Answer 1

Direction ratio of first line (3,2,3) and point (-4,0,1)

Direction of the second line (2,1,1) and point (0,1,-1)

Direction of the normal to the plane formed is cross product of this direction ratio= (3,2,3)x(2,1,1)=(-1,3,-1)

Equation of the plane : -x+3y-z=c

putting point(-4,0,1)

we get c=3

Equation of the plane is x-3y+z+3=0

For both the lines to pass through this plane other point must satisfy the plane's equation

(0,1,-1) does not satisfy the plane equation which means no plane can pass through the lines