Q.
If vector A→=cosωti^+sinωtj^ and B→=cosωt2i^+sinωt2j^ are functions of time, then the value of t at which they are orthogonal to each other is
see full answer
Start JEE / NEET / Foundation preparation at rupees 99/day !!
21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!
An Intiative by Sri Chaitanya
a
t=πω
b
t=0
c
t=π4ω
d
t=π2ω
answer is A.
(Unlock A.I Detailed Solution for FREE)
Ready to Test Your Skills?
Check your Performance Today with our Free Mock Test used by Toppers!
Take Free Test
Detailed Solution
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=πω
Watch 3-min video & get full concept clarity