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Tardigrade
Question
Mathematics
It p, q and r are non-zero, non-coplanar vectors then [p+q-r p-q q-r] = ldots
Q. It
p
,
q
and
r
are non-zero, non-coplanar vectors then
[
p
+
q
−
r
p
−
q
q
−
r
]
=
…
1813
206
MHT CET
MHT CET 2019
Report Error
A
3
[
p
q
r
]
B
0
C
[
p
q
r
]
D
2
[
p
q
r
]
Solution:
Given,
p
,
q
and
r
are non-zero coplanar vectors.
∴
[
p
+
q
−
r
p
−
q
q
−
r
]
=
(
p
+
q
−
r
)
⋅
[(
p
−
q
)
×
(
q
−
r
)]
=
(
p
+
q
−
r
)
⋅
[
p
×
q
−
p
×
r
−
q
×
q
+
q
×
r
]
=
(
p
+
q
−
r
)
⋅
[
p
×
q
−
p
×
r
+
q
×
r
]
(
∵
q
×
q
=
0
)
=
p
⋅
(
p
×
q
)
−
p
⋅
(
p
×
r
)
+
p
⋅
(
q
×
r
)
+
q
⋅
(
p
×
q
)
−
q
⋅
(
p
×
r
)
+
q
⋅
(
q
×
r
)
−
r
⋅
(
p
×
q
)
−
r
⋅
(
p
×
r
)
+
r
⋅
(
q
×
r
)
=
[
p
q
r
]
−
[
q
p
r
]
−
[
r
p
q
]
=
[
p
q
r
]
+
[
p
q
r
]
−
[
p
q
r
]
=
2
[
p
q
r
]
−
[
p
q
r
]
=
[
p
q
r
]