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Byju's Answer
Standard XII
Physics
Acceleration in 2D
If a⃗ = 4î-...
Question
If
→
a
=
4
^
i
−
6
^
j
,
→
b
=
5
^
i
−
^
j
and
→
c
=
−
^
j
then
(
→
a
×
→
c
)
⋅
→
b
=
A
−
6
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B
4
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C
0
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D
5
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Solution
The correct option is
C
0
Consider the problem
we have the vectors,
→
a
=
4
^
i
−
6
^
j
,
→
b
=
5
^
i
−
^
j
,
→
c
=
−
^
j
First we have to calculate,
→
a
×
→
c
Therefore,
→
a
×
→
c
=
∣
∣ ∣ ∣
∣
^
i
^
j
^
k
4
−
6
0
0
−
1
0
∣
∣ ∣ ∣
∣
Expanding along
C
3
Hence,
→
a
×
→
c
=
−
4
^
k
and now we have to calculate,
(
→
a
×
→
c
)
.
→
b
(
→
a
×
→
c
)
.
→
b
=
(
−
4
^
k
)
.
(
5
^
i
−
^
j
)
=
0
^
i
+
0
^
j
+
0
^
k
Hence, magnitude
=
√
0
2
+
0
2
+
0
2
=
0
Therefore,
∣
∣
(
→
a
×
→
c
)
.
→
b
∣
∣
=
0
Suggest Corrections
0
Similar questions
Q.
If
→
a
=
2
^
i
+
3
^
j
−
4
^
k
,
→
b
=
^
i
+
^
j
+
^
k
and
→
c
=
4
^
i
+
3
^
k
, then
|
→
a
×
(
→
b
×
→
c
)
|
=
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
=
^
i
−
2
^
j
+
^
k
and
→
b
=
^
i
−
^
j
+
^
k
be two vectors. If
→
c
is a vector such that
→
b
×
→
c
=
→
b
×
→
a
and
→
c
⋅
→
a
=
0
, then
→
c
⋅
→
b
is equal to :
Q.
If
→
a
=
^
i
+
^
j
+
^
k
,
→
b
=
^
i
+
^
j
−
^
k
,
→
c
=
^
i
−
^
j
+
^
k
and
→
d
=
^
i
−
^
j
−
^
k
, then
(
→
a
×
→
b
)
×
(
→
c
×
→
d
)
=
Q.
If
→
a
=
^
i
+
^
j
+
^
k
,
→
b
=
^
i
−
^
j
+
^
k
,
→
c
=
^
2
i
+
^
3
j
−
^
k
, then
(
→
a
×
→
b
)
×
→
c
=
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