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Exams
Joint Entrance Examination
Mathematics
Vector Algebra
Question 310
Question 310 of 379
Easy
MCQ
The vector
(
i
^
⋅
(
a
⃗
×
b
⃗
)
)
i
^
+
(
j
^
⋅
(
a
⃗
×
b
⃗
)
)
j
^
+
(
k
^
⋅
(
a
⃗
×
b
⃗
)
)
k
^
\big(\hat i\cdot(\vec a\times\vec b)\big)\hat i+\big(\hat j\cdot(\vec a\times\vec b)\big)\hat j+\big(\hat k\cdot(\vec a\times\vec b)\big)\hat k
(
i
^
⋅
(
a
×
b
)
)
i
^
+
(
j
^
⋅
(
a
×
b
)
)
j
^
+
(
k
^
⋅
(
a
×
b
)
)
k
^
is equal to:
A
b
⃗
×
a
⃗
\vec b\times\vec a
b
×
a
B
a
⃗
\vec a
a
C
a
⃗
×
b
⃗
\vec a\times\vec b
a
×
b
D
b
⃗
\vec b
b
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Official solution
For any vector
v
⃗
\vec v
v
,
(
v
⃗
⋅
i
^
)
i
^
+
(
v
⃗
⋅
j
^
)
j
^
+
(
v
⃗
⋅
k
^
)
k
^
=
v
⃗
(\vec v\cdot\hat i)\hat i+(\vec v\cdot\hat j)\hat j+(\vec v\cdot\hat k)\hat k=\vec v
(
v
⋅
i
^
)
i
^
+
(
v
⋅
j
^
)
j
^
+
(
v
⋅
k
^
)
k
^
=
v
. Applying this with
v
⃗
=
a
⃗
×
b
⃗
\vec v=\vec a\times\vec b
v
=
a
×
b
gives the sum
=
a
⃗
×
b
⃗
=\vec a\times\vec b
=
a
×
b
.
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