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Byju's Answer
Standard XII
Mathematics
Definition of Vector
Find the angl...
Question
Find the angle between the vectors
ˆ
i
−
2
ˆ
j
+
3
ˆ
k
and
3
ˆ
i
−
2
ˆ
j
+
ˆ
k
.
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Solution
Here, let
→
a
=
ˆ
i
−
2
ˆ
j
+
3
ˆ
k
and
→
b
=
3
ˆ
i
−
2
ˆ
j
+
ˆ
k
.
Then,
→
a
.
→
b
=
(
ˆ
i
−
2
ˆ
j
+
3
ˆ
k
)
.
(
3
ˆ
i
−
2
ˆ
j
+
ˆ
k
)
=
(
1.3
)
+
(
−
2
)
(
−
2
)
+
(
3.1
)
=
3
+
4
+
3
=
10
|
→
a
|
=
√
1
+
4
+
9
=
√
14
and,
|
→
b
|
=
√
9
+
4
+
1
=
√
14
Therefore,
cos
θ
=
10
√
14
√
14
=
10
14
=
5
7
Thus,
θ
=
cos
−
1
(
5
7
)
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1
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Q.
Find the angle between the vectors
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¯
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¯
O
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,
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