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Question : 2 of 91
Marks:
+1,
-0
Solution:
Two vectors
A and
B are orthogonal to each other, if their scalar product is zero i.e.
Aâ‹…B=0.
Here,
A=cos‌ω‌t‌+sin‌ωtand
B=cos‌+sin‌‌∴A⋅B=(cos‌ω‌t‌+sin‌ωt)(cos‌+sin‌‌)=cos‌ω‌t‌cos‌+sin‌ωtsin‌‌(∵⋅=⋅=1 and
⋅=⋅=0)=cos(ωt−‌)(∵cos(A−B)=cos‌A‌cos‌B+sin‌Asin‌B)But
Aâ‹…B=0 (as
A and
B are orthogonal to each other)
∴cos(ωt−‌)=0cos(ωt−‌)=cos‌ or
ωt−‌=‌‌=‌ or
t=‌
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