Question

Find the equation of the plane which contains twp parallel lines

Answer 1

a1/a2 = b1/b2 ≠ c1/c2

Answer 2

Solution :

The plane passes through the point (1,1,0)

Let the equation of the plane be :

a(x−1)+b(y−1)+c(z−0)=0------(1)

The line x−12=y+1−1=z3

It has direction ratios (2,−1,3)

∴a+b(−1−1)+3(3−0)=0

=>a−2b+3c=0------(2)

and 2a−b+3c=0--------(3)

Solving (2) and (3) we get

a−6+3=b+6−3=c−1+4

a=−3,b=3,c=3

substituting this in equ(1)

−3(x−1)+3(y−1)+3(z−0)

−3x+3+3y−3+3z=0

−3x+3y+3z=0

x−y−z=0 is the required equation of the plane

Let the equation of the plane be

a(x−1)+b(y+1)+c(z)=0

The line has direction ratios (2,−1,3)

a−3−6=b3−6=c4+1

a=−9,b=−3,c=5

Substituting in equ (1)

−9(x−1)−3(y+1)+5z=0

−9x+9−3y−3+5z=0

−9x−3y+5z+6=0

or 9x+3y−5z+6=0