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Let vecA=(hati+hatj)and,vecB=(2hati-hatj...

Let `vecA=(hati+hatj)and,vecB=(2hati-hatj)`. The magnitude of a coplanar vector `vecC` such that `vecA*vecC=vecB*vecC=vecA*vecB`, is given by :

A

`sqrt(5/9)`

B

`sqrt(10/9)`

C

`sqrt(20/9)`

D

`sqrt(9/12)`

Text Solution

Verified by Experts

The correct Answer is:
A
If `vecC=ahati+bhatj` then `vecA.vecC=vecA.vecB`
a+b=1 ….(i)
`vecB.vecC=vecA.vecB`
2a-b=1 ….(ii)
Solving equation (i) and (ii) we get
`a=1/3 , b=2/3`
`therefore` Magnitude of coplanar vector , `|vecC|=sqrt(1/9+4/9)=sqrt(5/9)`
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