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UPSEE 2019 Solved Paper
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© examsiri.com
Question :
132 of 150
Marks:
+1
,
-0
Let
p
,
q
,
r
be all distinct real numbers and the vectors
p
^
i
+
p
2
^
j
+
(
1
+
p
3
)
^
k
,
q
^
i
+
q
2
^
j
+
(
1
+
q
3
)
^
k
and
r
^
i
+
r
2
^
j
+
(
1
+
3
)
^
k
are coplanar. Then, pqr equals
2
1
- 1
−
2
Validate
Solution:
We have,
p
^
i
+
p
2
^
j
+
(
1
+
p
3
)
^
k
,
q
^
i
+
q
2
^
j
+
(
1
+
q
3
)
^
k
and
r
^
i
+
r
2
^
j
+
(
1
+
3
)
^
k
are coplanar.
∴
|
p
p
2
1
+
p
3
q
q
2
1
+
q
3
r
r
2
1
+
r
3
|
=
0
⇒
|
p
p
2
1
q
q
2
1
r
r
2
1
|
+
|
p
p
2
p
3
q
q
2
q
3
r
r
2
r
3
|
=
0
⇒
|
p
p
2
1
q
q
2
1
r
r
2
1
|
+
p
q
r
|
1
p
p
2
1
q
q
2
1
r
r
2
|
=
0
⇒
(
1
+
p
q
r
)
|
p
p
2
1
q
q
2
1
r
r
2
1
|
=
0
⇒
1
+
p
q
r
=
0
⇒
p
q
r
=
−
1
© examsiri.com
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