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NEET 2015 Physics and Chemistry Paper
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© examsnet.com
Question : 2
Total: 91
If vectors
→
A
=
cos
ω
t
^
i
+
s
i
n
ω
t
^
j
and
→
B
=
cos
ω
t
2
^
i
+
s
i
n
ω
t
2
^
j
are functions of time, then the value of
t
at which they are orthogonal to each other is
[NEET 2015]
t
=
π
ω
t
=
0
t
=
π
4
ω
t
=
π
2
ω
Validate
Solution:
👈: Video Solution
Two vectors
A
and
B
are orthogonal to each other, if their scalar product is zero i.e.
A
⋅
B
=
0
.
Here,
A
=
cos
ω
t
^
i
+
s
i
n
ω
t
^
j
and
B
=
cos
ω
t
2
^
i
+
s
i
n
ω
t
2
^
j
∴
A
⋅
B
=
(
cos
ω
t
^
i
+
s
i
n
ω
t
^
j
)
(
cos
ω
t
2
^
i
+
s
i
n
ω
t
2
^
j
)
=
cos
ω
t
cos
ω
t
2
+
s
i
n
ω
t
s
i
n
ω
t
2
(
∵
^
i
⋅
^
i
=
^
j
⋅
^
j
=
1
and
^
i
⋅
^
j
=
^
j
⋅
^
i
=
0
)
=
cos
(
ω
t
−
ω
t
2
)
(
∵
cos
(
A
−
B
)
=
cos
A
cos
B
+
s
i
n
A
s
i
n
B
)
But
A
⋅
B
=
0
(as
A
and
B
are orthogonal to each other)
∴
cos
(
ω
t
−
ω
t
2
)
=
0
cos
(
ω
t
−
ω
t
2
)
=
cos
π
2
or
ω
t
−
ω
t
2
=
π
2
ω
t
2
=
π
2
or
t
=
π
ω
© examsnet.com
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