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Byju's Answer
Standard XII
Mathematics
Angle between Two Lines
Vector A⃗ ,...
Question
Vector
→
A
,
→
B
,
and
→
C
are shown in figure.
Find angle between:
→
A
a
n
d
→
B
→
A
a
n
d
→
C
→
B
a
n
d
→
C
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Solution
From the diagram,
Angle between
→
A
and
→
B
is
60
+
45
=
105
∘
Angle between
→
A
and
→
C
is
30
+
30
+
90
=
150
∘
Angle between
→
C
and
→
B
is
60
+
45
=
105
∘
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Similar questions
Q.
If
→
a
=
^
i
+
^
j
+
^
k
,
→
b
=
^
j
−
^
k
, then find a vector
→
c
such that
→
a
×
→
c
=
→
b
a
n
d
→
a
.
→
c
=
3
.
Q.
If the magnitude of vectors
→
A
,
→
B
and
→
C
are
12
,
5
and
13
units, respectively, and
→
A
+
→
B
=
→
C
, the angle between vectors
→
A
a
n
d
→
B
is:
Q.
Vectors
→
a
,
→
b
and
→
c
are such that
→
a
+
→
b
+
→
c
=
→
0
and
|
→
a
|
=
3
,
|
→
b
=
5
and
|
→
c
|
=
7
. Find the angle between
→
a
and
→
b
.
Q.
If
→
a
and
→
b
are perpendicular unit vectors and vector
→
c
is such that
→
c
=
→
a
+
→
b
, then
(
→
a
×
→
b
)
.
(
→
b
×
→
c
)
+
(
→
b
×
→
c
)
.
(
→
c
×
→
a
)
+
(
→
c
×
→
a
)
.
(
→
a
×
→
b
)
is
Q.
Let
→
a
,
→
b
,
→
c
be vectors of length
3
,
4
and
5
respectively. Let
→
a
be perpendicular to
(
→
b
+
→
c
)
,
→
b
to
(
→
c
+
→
a
)
and
→
c
to
(
→
a
+
→
b
)
. Find the length of the vector
→
a
+
→
b
+
→
c
.
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