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Byju's Answer
Standard X
Geography
India - Location, Latitudinal and Longitudinal Extent
The value of ...
Question
The value of (\overrightarrow P +\overrightarrow Q) x (\overrightarrow P -\overrightarrow Q
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Q.
Let
→
p
,
→
q
,
→
r
be three mutually perpendicular vectors of the same magnitude. If a vector
→
x
satisfies the equation
→
p
[
(
→
x
−
→
q
)
×
→
p
]
+
→
q
×
[
(
→
x
−
→
r
)
×
→
q
]
+
→
r
×
[
(
→
x
−
→
p
)
×
→
r
]
=
→
0
, then
→
x
is given by
Q.
For non-zero vectors
→
p
,
→
q
and
→
r
,
let
(
→
p
×
→
q
)
×
→
r
+
(
→
q
⋅
→
r
)
→
q
=
(
x
2
+
y
2
)
→
q
+
(
14
−
4
x
−
6
y
)
→
p
and
(
→
r
⋅
→
r
)
→
p
=
→
r
where
→
p
and
→
q
are non-collinear, and
x
and
y
are scalars. Then the value of
(
x
+
y
)
is
Q.
Three vectors
→
P
,
→
Q
and
→
R
are such that
|
→
P
|
=
|
→
Q
|
,
|
→
R
|
=
√
2
|
→
P
|
, and
→
P
+
→
Q
+
→
R
=
→
0
. The angles between
→
P
and
→
Q
,
→
Q
and
→
R
, and
→
P
and
→
R
are
Q.
Three vectors
→
P
,
→
Q
and
→
R
are such that
|
→
P
|
=
|
→
Q
|
,
|
→
R
|
=
√
2
|
→
P
|
and
→
P
+
→
Q
+
→
R
=
0
. The angle between
→
P
and
→
Q
,
→
Q
and
→
R
, and
→
P
and
→
R
are
Q.
Let
(
→
p
×
→
q
)
×
→
r
+
(
→
q
⋅
→
r
)
→
q
=
(
x
2
+
y
2
)
→
q
+
(
14
−
4
x
−
6
y
)
→
p
and
(
→
r
⋅
→
r
)
→
p
=
→
r
where
→
p
and
→
q
are two non-zero non-collinear vectors, and
x
and
y
are scalars. Then the value of
(
x
+
y
)
is
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