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if a i 2j 3k b 3i j 2k then the angle between a b
Question:
If
a
→
=
i
^
+
2
j
^
−
3
k
^
,
b
→
=
3
i
^
−
j
^
+
2
k
^
then the angle between
a
→
+
b
→
,
a
→
−
b
→
is:
MHT CET
Updated On:
May 4, 2024
(A)
0
∘
(B)
180
∘
(C)
90
∘
(D)
−
180
∘
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Verified By Collegedunia
The Correct Option is
C
Solution and Explanation
Explanation:
Given:
a
→
=
i
^
+
2
j
^
−
3
k
^
b
→
=
3
i
^
−
j
^
+
2
k
^
So,
(
a
→
+
b
→
)
=
i
^
+
2
j
^
−
3
k
^
+
3
i
^
−
j
^
+
2
k
^
(
a
→
+
b
→
)
=
(
i
^
+
3
i
^
)
+
(
2
j
^
−
j
^
)
+
(
−
3
k
^
+
2
k
^
)
a
→
+
b
→
=
4
i
^
+
j
^
−
k
^
(
a
→
−
b
→
)
=
i
^
+
2
j
^
−
3
k
^
−
3
i
^
−
j
^
+
2
k
^
(
a
→
−
b
→
)
=
(
i
^
−
3
i
^
)
+
(
2
j
^
−
(
−
j
)
^
)
+
(
−
3
k
^
−
2
k
^
)
⇒
a
→
−
b
→
=
−
2
i
^
+
3
j
^
−
5
k
^
Then,
(
a
→
+
b
→
)
⋅
(
a
→
−
b
→
)
=
(
4
i
^
+
j
^
−
k
^
)
⋅
(
−
2
i
^
+
3
j
^
−
5
k
^
)
(
a
→
+
b
→
)
⋅
(
a
→
−
b
→
)
=
−
8
+
3
+
5
=
0
If
(
a
→
+
b
→
)
⋅
(
a
→
−
b
→
)
=
0
Then angle between two vectors is
90
∘
.Hence, the correct option is (C).
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