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find the angle between two vectors a 2i j 3k and b
Question:
Find the angle between two vectors
(
a
→
=
2
i
^
+
j
^
−
3
k
^
)
and
(
b
→
=
3
i
^
−
2
j
^
−
k
^
)
.
MHT CET
Updated On:
Mar 29, 2024
(A)
−
160
∘
(B)
−
60
∘
(C)
160
∘
(D)
60
∘
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The Correct Option is
D
Solution and Explanation
Explanation:
Given:
a
→
=
2
i
^
+
j
^
−
3
k
^
and
b
→
=
3
i
^
−
2
j
^
−
k
^
a
→
⋅
b
→
=
(
2
i
^
+
j
^
−
3
k
^
)
(
3
i
^
−
2
j
^
−
k
^
)
=
6
−
2
+
3
=
7
…
.
(
1
)
|
a
→
|
=
2
2
+
1
2
+
(
−
3
)
2
=
14
…
(
2
)
|
b
→
|
=
3
2
+
(
−
2
)
2
+
(
−
1
)
2
=
14
…
.
(
3
)
cos
θ
=
a
→
⋅
b
→
|
a
→
|
⋅
|
b
→
|
Put the values from (1), (2) amnd (3) in above equation:
=
7
14
.
14
=
1
2
cos
θ
=
cos
60
∘
θ
=
60
∘
Hence, the correct option is (D).
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