The vectors Ä is given by Ā=tî - (sinnt)j + t?k where t is time. Then which of the following is (are) correct?
(A) |Ā) (at t = 1) = V2
dĀ
(at t = 1) = i + 1] + 2K
dt
(at t = 1) = V272 +1
dĀ
(at t = 1) = 3
con la sua
(D) Ā.
dt
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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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