Answer
Hence, possible values of ‘a’ are 5 or –3.
Step-by-step explanation:
The distance between two points
P
(
x
1
,
y
1
,
z
1
)
and
Q
(
x
2
,
y
2
,
z
2
)
is given by
P
Q
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
+
(
z
2
−
z
1
)
2
The distance between two points
(
a
,
2
,
1
)
and
(
1
,
–
1
,
1
)
is given as 5.
∴
√
(
a
−
1
)
2
+
(
2
+
1
)
2
+
(
1
−
1
)
2
=
5
⇒
(
a
−
1
)
2
+
9
=
25
⇒
(
a
−
1
)
2
=
16
⇒
a
−
1
=
4
o
r
a
−
1
=
−
4
⇒
(
a
=
5
)
o
r
(a=−3)
