x+13=y+35=z+57 ......(i)
and x−21=y−43=z−65 .......(ii)
Condition for coplanar, then
∣∣
∣∣x2−x1y2−y1z2−z1l1m1n1l2m2n2∣∣
∣∣=0
∣∣
∣∣2+14+36+5357135∣∣
∣∣
=∣∣
∣∣3711357135∣∣
∣∣
⇒3(25−21)−7(15−7)+11(9−5)
⇒3(4)−7×8+11(4)
⇒12−56+44
⇒56−56=0
Let x+13=y+35=z+57=r1
x=3r1−1
y=5r1−3
z=7r1−5
and from (ii) x−21=y−43=z−65=r2
x=r2+2
y=3r2+4
z=5r2+6
3r1−1=r2+2
3r1−r2=2+1=3 ....(i)
5r1−3=3r2+4
5r1−3r2=7 ......(ii)
3r1−r2=3×5
5r1−3r2=7×4
____________________
15r1−5r2=15
15r1−9r2=21
- + -
____________________
4r2=−6
r2=−64=−32,r2=−32
3r1−r2=3
3r1+32=3
3r1=3−32=32
r1=32×13=12
r1=12,r2=−32
x=3r1−1=3×12−1
x=12
y=5r1−3
y=512−3=52−3
y=−12
z=7r1−5
z=7×12−5=72−5
z=−32
x=12
y=−12
z=−32.