10 Find the angle between the following pairs of lines:
(i)
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
2
5
(3
2
6 )
r
i
j
k
i
j
k
=
−
+
+ λ
+
+
r
 and
ˆ
ˆ
ˆ
ˆ
ˆ
7
6
(
2
2 )
r
i
k
i
j
k
=
−
+ µ
+
+
r
(ii)
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
3
2
(
2 )
r
i
j
k
i
j
k
=
+
−
+ λ
−
−
r
 and
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
2
56
(3
5
4 )
r
i
j
k
i
j
k
=
−
−
+ µ
−
−
r
11 Find the angle between the following pair of lines:
(i)
2
1
3
2
4
5
and
2
5
3
1
8
4
x
y
z
x
y
z
−
− +
+
−
−
=
=
=
=
−
−
(ii)
5
2
3
and
2
2
1
4
1
8
x
y
z
x
y
z
−
−
−
=
=
=
=
12 Find the values of p so that the lines 1
7
14
3
3
2
2
x
y
z
p
−
−
−
=
=
and  7
7
5
6
3
1
5
x
y
z
p
−
−
−
=
=
 are at right angles