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Byju's Answer
Standard XII
Mathematics
Vector Triple Product
If a⃗ = î +...
Question
If
→
a
=
^
i
+
2
^
j
+
3
^
k
,
→
b
=
2
^
i
−
^
j
+
^
k
and
→
c
=
3
^
i
+
2
^
j
+
^
k
and
→
a
×
(
→
b
×
→
c
)
is equal to
x
→
a
+
y
→
b
+
z
→
c
, then
x
+
y
+
z
is equal to
Open in App
Solution
→
b
×
→
c
=
∣
∣ ∣ ∣
∣
^
i
^
j
^
k
2
−
1
1
3
2
1
∣
∣ ∣ ∣
∣
=
^
i
(
−
1
−
2
)
−
^
j
(
2
−
3
)
+
^
k
(
4
+
3
)
=
−
3
^
i
+
^
j
+
7
^
k
→
a
×
(
→
b
×
→
c
)
=
∣
∣ ∣ ∣
∣
^
i
^
j
^
k
1
2
3
−
3
1
7
∣
∣ ∣ ∣
∣
=
11
^
i
−
16
^
j
+
7
^
k
Given that
→
a
×
(
→
b
×
→
c
)
=
x
→
a
+
y
→
b
+
z
→
c
x
+
2
y
+
3
z
=
11
−
−
−
−
(
1
)
2
x
−
y
+
2
z
=
−
16
−
−
−
−
(
2
)
3
x
+
y
+
z
=
7
−
−
−
−
(
3
)
Adding
(
1
)
with
2
×
(
2
)
we get,
5
x
+
7
z
=
−
21
----
(
4
)
Adding
(
3
)
with
(
2
)
5
x
+
3
z
=
−
9
----
(
5
)
Subtracting
(
4
)
from
(
5
)
, we get,
z
=
−
3
from
(
5
)
5
x
+
3
z
=
−
9
5
x
+
3
×
−
3
=
−
9
x
=
0
from
(
1
)
x
=
2
y
+
3
z
=
11
0
+
2
y
+
3
×
−
3
=
11
y
=
10
therefore,
x
+
y
+
z
=
7
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0
Similar questions
Q.
Given
→
p
=
3
^
i
+
2
^
j
+
4
^
k
,
→
a
=
^
i
+
^
j
,
→
b
=
^
j
+
^
k
,
→
c
=
^
i
+
^
k
and
→
P
=
x
→
a
+
y
→
b
+
z
→
c
, then
x
,
y
,
z
are respectively.
Q.
If
→
a
=
2
^
i
+
^
j
+
3
^
k
,
→
b
=
3
^
i
+
2
^
j
+
^
k
,
→
c
=
^
i
−
^
j
−
4
^
k
,
→
d
=
^
i
+
2
^
j
−
^
k
, then
(
→
a
×
→
b
)
×
(
→
c
×
→
d
)
=
Q.
Find
→
a
⋅
(
→
b
×
→
c
)
, if
→
a
=
2
^
i
+
^
j
+
3
^
k
,
→
b
=
−
^
i
+
2
^
j
+
^
k
and
→
c
=
3
^
i
+
^
j
+
2
^
k
.
Q.
I: If
→
a
=
3
^
i
−
2
^
j
+
^
k
,
→
b
=
2
^
i
−
4
^
j
−
3
^
k
,
→
c
=
−
^
i
+
2
^
j
+
2
^
k
then
→
a
+
→
b
+
→
c
=
4
^
i
−
4
^
j
II: If
→
a
=
^
i
−
^
j
+
2
^
k
,
→
b
=
2
^
i
+
3
^
j
+
^
k
,
→
c
=
^
i
−
^
k
, then magnitude of
→
a
+
2
→
b
−
3
→
c
is
√
78
Q.
If
→
a
=
2
^
i
+
^
j
+
3
^
k
,
→
b
=
−
^
i
+
2
^
j
+
^
k
and
→
c
=
3
^
i
+
^
j
+
2
^
k
. Find
→
a
⋅
(
→
b
×
→
c
)
.
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