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Byju's Answer
Standard XII
Mathematics
Collinear Vectors
â and b̂ ar...
Question
^
a
and
^
b
are mutually perpendicular unit vectors. If
^
r
is a vector satisfying
^
r
.
^
a
=
0
,
^
r
.
^
b
=
1
,
and
[
r
a
b
]
=
1
, then
^
r
is
A
^
a
×
^
b
+
^
b
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B
^
a
+
^
b
×
^
a
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C
^
a
×
^
b
−
^
b
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D
none of these
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Solution
The correct option is
A
^
a
×
^
b
+
^
b
Let
r
=
x
1
a
+
x
2
b
+
x
3
(
a
×
b
)
Then,
r
.
a
=
x
1
|
a
|
2
,
r
.
b
=
x
2
|
b
|
2
and,
r
.
(
a
×
b
)
=
x
3
|
a
×
b
|
2
⇒
x
1
=
0
,
x
2
=
1
,
x
3
=
1
∴
r
=
a
×
b
+
b
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0
Similar questions
Q.
If
^
a
,
^
b
and
^
c
are unit vectors satisfying
|
^
a
−
^
b
|
2
+
|
^
b
−
^
c
|
2
+
|
^
c
−
^
a
|
2
=
9
, then
|
2
^
a
+
5
^
b
+
5
^
c
|
is
Q.
Arrange the value of
|
a
+
b
+
c
|
in ascending order
A
.If
^
a
,
^
b
,
^
c
are mutually perpendicular unit vectors
B
. If
^
a
,
^
b
,
^
c
are vectors of lengths 2,3,4 respectively and
^
a
,
^
b
,
^
c
are perpendicular to
^
b
+
^
c
,
^
c
+
^
a
,
^
a
+
^
b
respectively.
C
. If
^
a
,
^
b
,
^
c
are vectors of lengths 4,4,5 respectively and
^
a
,
^
b
,
^
c
are perpendicular to
^
b
+
^
c
,
^
c
+
^
a
,
^
a
+
^
b
respectively.
Q.
If
^
a
and
^
b
are two unit vectors, then the vector
(
^
a
+
^
b
)
×
(
^
a
×
^
b
)
is parallel to
Q.
If
^
a
,
^
b
,
^
c
are mutually perpendicular unit vectors, then
∣
∣
^
a
+
^
b
+
^
c
∣
∣
is equal to
Q.
If three unit vector
^
a
,
^
b
,
^
c
satisfy
^
a
+
^
b
+
^
c
=
^
0
, then the angle between
^
a
and
^
b
is
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