are mutually perpendicular. As we know that, if a, b, c are the direction ration ratios of a line passing through the point (x1,y1,z1), then the equation of line is given by:
x−x1
a
=
y−y1
b
=
z−z1
c
‌‌
x−x1
a
=
y−y1
b
=
z−z1
c
Let L1:
x−1
−3
=
y−2
2k
=
z−3
2
‌
x−1
−3
=
y−2
2k
=
z−3
2
and L2=
x−1
3k
=
y−5
1
=
z−6
−5
‌‌
x−1
3k
=
y−5
1
=
z−6
−5
Now by comparing L1 and L2 with
x−x1
a
=
y−y1
b
=
z−z1
c
‌‌‌
x−x1
a
=
y−y1
b
=
z−z1
c
we get ⇒a1=−3,b1=2k,c1=2,a2=3k,b2=1 and c2=−5 As we know that if two lines are perpendicular then a1.a2+b1.b2+c1.c2=0 ⇒a1.a2+b1.b2+c1.c2=−9k+2k−10=0 ⇒ - 7k = 10 ⇒ k = - 10/7 Hence, option A is the correct answer