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Byju's Answer
Standard XII
Mathematics
Applications of Cross Product
If a⃗=4î+4ĵ...
Question
If
→
a
=
4
^
i
+
4
^
j
−
7
^
k
, then the value of
^
i
×
(
→
a
×
^
i
)
+
^
j
×
(
→
a
×
^
j
)
+
^
k
×
(
→
a
×
^
k
)
=
A
4
^
i
+
4
^
j
−
7
^
k
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B
8
^
i
+
8
^
j
−
14
^
k
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C
8
^
i
−
8
^
j
−
14
^
k
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D
4
^
i
−
4
^
j
−
7
^
k
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Solution
The correct option is
D
8
^
i
+
8
^
j
−
14
^
k
(
i
×
(
→
a
×
i
)
)
+
(
j
×
(
→
a
×
j
)
)
+
(
k
×
(
→
a
×
k
)
)
=
(
→
a
(
i
.
i
)
−
i
(
→
a
.
i
)
)
+
(
→
a
(
j
.
j
)
−
i
(
→
a
.
j
)
)
+
(
→
a
(
k
.
k
i
)
−
i
(
→
a
.
k
)
)
=
→
a
+
i
(
a
x
)
+
→
a
+
j
(
a
y
)
+
→
a
+
k
(
a
z
)
=
3
→
a
+
i
a
x
+
j
a
y
+
k
a
z
=
3
→
a
+
→
a
=
2
→
a
=
2
(
4
i
+
4
j
−
7
k
)
=
8
i
+
8
j
−
14
k
Suggest Corrections
0
Similar questions
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.
Find the sum of the vectors
→
a
=
^
i
−
2
^
j
+
^
k
=
−
2
^
i
+
4
^
j
+
5
^
k
and
→
c
=
^
i
−
6
^
j
−
7
^
k
.
Q.
If
→
a
=
3
^
j
−
2
^
j
+
7
^
k
,
→
b
=
5
^
i
+
^
j
−
2
^
k
and
→
c
=
^
i
+
^
j
−
^
k
, then find
→
a
⋅
(
→
b
×
→
c
)
.
Q.
Let
→
a
=
2
^
i
+
^
k
,
→
b
=
^
i
+
^
j
+
^
k
and
→
c
=
4
^
i
−
3
^
j
+
7
^
k
be three vectors. The vector which satisfies
→
r
×
→
b
=
→
c
×
→
b
and
→
r
.
→
a
=
0
is
Q.
The projection of the vector
^
i
−
2
^
j
+
^
k
on the vector
4
^
i
−
4
^
j
+
7
^
k
is
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