(1) Which of the following function is orthogonal to each other?
(i) /y2y2dı = 0
(ii) Jyly2dt = 0
ilyly2dt = 1
(iv) ſw2w2dt = 1.
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11th
Physics
Work, Energy and Power
Scalar Product
If vectors A = cos ω t î +...
PHYSICS
If vectors A=cosωt
i
^
+sin
j
^
and B=cos
2
ωt
i
^
+sin
2
ωt
j
^
are functions of time, then the value of t at which they are orthogonal to each other
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ANSWER
Given,
A
=(coswt
i
^
+sinw
j
^
)⋅
B
=(cos
2
wt
i
^
+sin
2
wt
j
^
)
When they are orthogonal, their dot product will e zero
A
⋅
B
=(coswt
i
^
+sinwt
j
^
)⋅(cos
2
wt
i
^
+sin
2
wt
j)
0=cos(wt−
2
wt
)
cos(wt−
2
wt
)=0=
2
π
cos(
2
wt
)=
2
π
2
wt
=
2
π
t=
w
π
Hence, value of time is
ω
π
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