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Byju's Answer
Other
Engineering Mathematics
Vector Identities
▽×▽× P where ...
Question
▽
×
▽
×
P
(where
P
is a vector) is equal to
A
P
×
▽
×
P
−
▽
2
P
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B
▽
2
P
+
▽
(
▽
×
P
)
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C
▽
2
P
+
▽
×
P
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D
▽
(
▽
.
P
)
−
▽
2
P
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Solution
The correct option is
D
▽
(
▽
.
P
)
−
▽
2
P
▽
×
(
▽
×
P
)
=
(
▽
.
P
)
▽
−
(
▽
.
▽
)
P
(Using vector identify)
=
▽
(
▽
.
P
)
−
▽
2
P
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2
Similar questions
Q.
∫
∫
(
∇
×
P
)
.
d
S
,
Where P is a vector, is equal to
Q.
The vectors
→
x
and
→
y
satisfy the equation
p
→
x
+
q
→
y
=
→
a
(where
p
,
q
are scalar constants and
→
a
is a known vector). It is given that
→
x
.
→
y
≥
|
→
a
|
2
4
p
q
, then
|
→
x
|
|
→
y
|
is equal to (
p
q
>
0
)
Q.
Let
L
=
⎡
⎢
⎣
2
3
5
4
1
2
1
2
1
⎤
⎥
⎦
=
P
+
Q
,
where
P
is a symmetric matrix &
Q
is a skew-symmetric matrix, then
P
is equal to
Q.
The value of the quantity
P
where
P
=
∫
1
0
x
e
x
d
x
,
is equal to
Q.
Let
→
p
=
2
^
i
+
3
^
j
+
^
k
and
→
q
=
^
i
+
2
^
j
+
^
k
be two vectors. If a vector
→
r
=
α
^
i
+
β
^
j
+
γ
^
k
is perpendicular to each of the vectors
(
→
p
+
→
q
)
and
(
→
p
−
→
q
)
,
and
∣
∣
→
r
∣
∣
=
√
3
,
then
|
α
|
+
|
β
|
+
|
γ
|
is equal to
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