Questions
If vector and are functions of time, then the value of t at which they are orthogonal to each other is
detailed solution
Correct option is A
Two vectors A→ and B→ are orthogonal to each other, if their scalar product is zero i.e. A→·B→=0 . Here, A→=cosωti^+sinωtj^ and B→=cosωt2i^+sinωt2j^∴A→·B→=(cosωti^+sinωtj^)·cosωt2i^+sinωt2j^=cosωtcosωt2+sinωtsinωt2(∵i^·i^=j^·j^=1 and i^·j^=j^·i^=0)=cosωt-ωt2(∵cos(A-B)=cosAcosB+sinAsinB) But A→·B→=0 (as A→ and B→ are orthogonal to each other) ∴ cosωt-ωt2=0cosωt-ωt2=cosπ2 or ωt-ωt2=π2ωt2=π2 or t=πωSimilar Questions
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