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Byju's Answer
Standard XII
Mathematics
Multiplication of Matrices
Find the volu...
Question
Find the volume of the parallelopiped whose coterminous edges are represented by the vectors:
(i)
a
→
=
2
i
^
+
3
j
^
+
4
k
^
,
b
→
=
i
^
+
2
j
^
-
k
^
,
c
→
=
3
i
^
-
j
^
+
2
k
^
(ii)
a
→
=
2
i
^
-
3
j
^
+
4
k
^
,
b
→
=
i
^
+
2
j
^
-
k
^
,
c
→
=
3
i
^
-
j
^
-
2
k
^
(iii)
a
→
=
11
i
^
,
b
→
=
2
j
^
,
c
→
=
13
k
^
(iv)
a
→
=
i
^
+
j
^
+
k
^
,
b
→
=
i
^
-
j
^
+
k
^
,
c
→
=
i
^
+
2
j
^
-
k
^
Open in App
Solution
i
Given
:
a
→
=
2
i
^
+
3
j
^
+
4
k
^
b
→
=
i
^
+
2
j
^
-
k
^
c
→
=
3
i
^
-
j
^
+
2
k
^
We
know
that
the
volume
of
a
parallelopiped
whose
three
adjacent
edges
are
a
→
,
b
→
,
c
→
is
equal
to
a
→
b
→
c
→
.
Here
,
a
→
b
→
c
→
=
2
3
4
1
2
-
1
3
-
1
2
=
2
4
-
1
-
3
2
+
3
+
4
-
1
-
6
=
-
37
Volume
of
the
parallelopiped
=
a
→
b
→
c
→
=
-
37
=
37
cubic
units
ii
Given
:
a
→
=
2
i
^
-
3
j
^
+
4
k
^
b
→
=
i
^
+
2
j
^
-
k
^
c
→
=
3
i
^
-
j
^
-
2
k
^
We
know
that
the
volume
of
a
parallelopiped
whose
three
adjacent
edges
are
a
→
,
b
→
,
c
→
is
equal
to
a
→
b
→
c
→
.
Here
,
a
→
b
→
c
→
=
2
-
3
4
1
2
-
1
3
-
1
-
2
=
2
-
4
-
1
+
3
-
2
+
3
+
4
-
1
-
6
=
-
35
Volume
of
the
parallelopiped
=
a
→
b
→
c
→
=
-
35
=
35
cubic
units
iii
Given
:
a
→
=
11
i
^
b
→
=
2
j
^
c
→
=
13
k
^
We
know
that
the
volume
of
a
parallelopiped
whose
three
adjacent
edges
are
a
→
,
b
→
,
c
→
is
equal
to
a
→
b
→
c
→
.
Here
,
a
→
b
→
c
→
=
11
0
0
0
2
0
0
0
13
=
11
26
-
0
-
0
0
-
0
+
0
0
-
0
=
286
Volume
of
the
parallelopiped
=
a
→
b
→
c
→
=
286
=
286
cubic
units
iv
Given
:
a
→
=
i
^
+
j
^
+
k
^
b
→
=
i
^
-
j
^
+
k
c
→
=
i
^
+
2
j
-
k
^
We
know
that
the
volume
of
a
parallelopiped
whose
three
adjacent
edges
are
a
→
,
b
→
,
c
→
is
equal
to
a
→
b
→
c
→
.
Here
,
a
→
b
→
c
→
=
1
1
1
1
-
1
1
1
2
-
1
=
1
1
-
2
-
1
-
1
-
1
+
1
2
+
1
=
4
Volume
of
the
parallelopiped
=
a
→
b
→
c
→
=
4
=
4
cubic
units
Suggest Corrections
0
Similar questions
Q.
Find the volume of the parallelopiped whose coterminous edges are represented by
a
=
2
i
−
3
j
+
4
k
,
b
=
i
+
2
j
−
k
,
c
=
3
i
−
j
+
2
k
Q.
Find
a
→
b
→
c
→
, when
(i)
a
→
=
2
i
^
-
3
j
^
,
b
→
=
i
^
+
j
^
-
k
^
and
c
→
=
3
i
^
-
k
^
(ii)
a
→
=
i
^
-
2
j
^
+
3
k
^
,
b
→
=
2
i
^
+
j
^
-
k
^
and
c
→
=
j
^
+
k
^
(iii)
a
→
=
2
i
^
+
3
j
^
+
k
^
,
b
→
=
i
^
-
2
j
^
+
k
^
and
c
→
=
-
3
i
^
+
j
^
+
2
k
^
Q.
If the volume of parallelopiped whose coterminous edges are
¯
¯
¯
a
=
3
¯
i
−
¯
j
+
4
¯
¯
¯
k
,
¯
¯
b
=
2
¯
i
+
3
¯
j
−
¯
¯
¯
k
and
¯
¯
c
=
−
5
¯
i
+
2
¯
j
+
3
¯
¯
¯
k
is three times the volume of parallelopiped whose coterminous edges are
¯
¯
¯
p
=
¯
i
+
¯
j
+
3
¯
¯
¯
k
,
¯
¯
¯
q
=
¯
i
−
2
¯
j
+
λ
¯
¯
¯
k
and
¯
¯
¯
r
=
2
¯
i
+
3
¯
j
then the value of
λ
is
Q.
Find the value of λ so that the following vectors are coplanar:
(i)
a
→
=
i
^
-
j
^
+
k
^
,
b
→
=
2
i
^
+
j
^
-
k
^
,
c
→
=
λ
i
^
-
j
^
+
λ
k
^
(ii)
a
→
=
2
i
^
-
j
^
+
k
^
,
b
→
=
i
^
+
2
j
^
-
3
k
^
,
c
→
=
λ
i
^
+
λ
j
^
+
5
k
^
(iii)
a
→
=
i
^
+
2
j
^
-
3
k
^
,
b
→
=
3
i
^
+
λ
j
^
+
k
^
,
c
→
=
i
^
+
2
j
^
+
2
k
^
(iv)
a
→
=
i
^
+
3
j
^
,
b
→
=
5
k
^
,
c
→
=
λ
i
^
-
j
^
Q.
Prove that the following vectors are coplanar:
(i)
2
i
^
-
j
^
+
k
^
,
i
^
-
3
j
^
-
5
k
^
and
3
i
^
-
4
j
^
-
4
k
^
(ii)
i
^
+
j
^
+
k
^
,
2
i
^
+
3
j
^
-
k
^
and
-
i
^
-
2
j
^
+
2
k
^
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