1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Vector Triple Product
Show the each...
Question
Show the each of the following triads of vectors are coplanar:
(i)
a
→
=
i
^
+
2
j
^
-
k
^
,
b
→
=
3
i
^
+
2
j
^
+
7
k
^
,
c
→
=
5
i
^
+
6
j
^
+
5
k
^
(ii)
a
→
=
-
4
i
^
-
6
j
^
-
2
k
^
,
b
→
=
-
i
^
+
4
j
^
+
3
k
^
,
c
→
=
-
8
i
^
-
j
^
+
3
k
^
(iii)
a
^
=
i
^
-
2
j
^
+
3
k
^
,
b
^
=
-
2
i
^
+
3
j
^
-
4
k
^
,
c
^
=
i
^
-
3
j
^
+
5
k
^
Open in App
Solution
i
Given
:
a
→
=
i
^
+
2
j
^
-
k
^
b
→
=
3
i
^
+
2
j
^
+
7
k
^
c
→
=
5
i
^
+
6
j
^
+
5
k
^
We
know
that
three
vectors
a
→
,
b
→
,
c
→
are
coplanar
iff
their
scalar
triple
product
is
zero
,
i
.
e
.
a
→
b
→
c
→
=
0
Here
,
a
→
b
→
c
→
=
1
2
-
1
3
2
7
5
6
5
=
1
10
-
42
-
2
15
-
35
-
1
18
-
10
=
0
Hence
,
the
given
vectors
are
coplanar
.
ii
Given
:
a
→
=
-
4
i
^
-
6
j
^
-
2
k
^
b
→
=
-
i
^
+
4
j
^
+
3
k
^
c
→
=
-
8
i
^
-
j
^
+
3
k
^
We
know
that
three
vectors
a
→
,
b
→
,
c
→
are
coplanar
iff
their
scalar
triple
product
is
zero
,
i
.
e
.
a
→
b
→
c
→
=
0
.
Here
,
a
→
b
→
c
→
=
-
4
-
6
-
2
-
1
4
3
-
8
-
1
3
=
-
4
12
+
3
+
6
-
3
+
24
-
2
1
+
32
=
0
Hence
,
the
given
vectors
are
coplanar
.
iii
Given
:
a
→
=
i
^
-
2
j
^
+
3
k
^
b
→
=
-
2
i
^
+
3
j
^
-
4
k
^
c
→
=
i
^
-
3
j
^
+
5
k
^
We
know
that
three
vectors
a
→
,
b
→
,
c
→
are
coplanar
iff
their
scalar
triple
product
is
zero
,
i
.
e
.
a
→
b
→
c
→
=
0
.
Here
,
a
→
b
→
c
→
=
1
-
2
3
-
2
3
-
4
1
-
3
5
=
1
15
-
12
+
2
-
10
+
4
+
3
6
-
3
=
0
Hence
,
the
given
vectors
are
coplanar
.
Suggest Corrections
0
Similar questions
Q.
Show the each of the following triads of vectors are coplanar:
(i)
a
→
=
i
^
+
2
j
^
-
k
^
,
b
→
=
3
i
^
+
2
j
^
+
7
k
^
,
c
→
=
5
i
^
+
6
j
^
+
5
k
^
(ii)
a
→
=
-
4
i
^
-
6
j
^
-
2
k
^
,
b
→
=
-
i
^
+
4
j
^
+
3
k
^
,
c
→
=
-
8
i
^
-
j
^
+
3
k
^
(iii)
a
^
=
i
^
-
2
j
^
+
3
k
^
,
b
^
=
-
2
i
^
+
3
j
^
-
4
k
^
,
c
^
=
i
^
-
3
j
^
+
5
k
^
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.
The unit vector in the direction of sum of the vectors
→
A
=
2
ˆ
i
+
4
ˆ
j
−
7
ˆ
k
and
→
B
=
4
ˆ
i
−
6
ˆ
j
+
4
ˆ
k
will be
