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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((9)/(12))`

B

`sqrt((5)/(9))`

C

`sqrt((10)/(9))`

D

`sqrt((10)/(9))`

Text Solution

Verified by Experts

The correct Answer is:
C
(c): Vector `vecC` is given to be coplanar with `vecA and vecB` , hence vector `vecC` must have only x and y components.
Let `vecC=xhati+yhatj` then
`vecA.vecC=vecA.vecB`
`x+y=1`
`vecB.vecC=vecA.vecB`
`2x-y=1`
Solving equation (i) and (ii) we get
`x=(1)/(3), y=(2)/(3)`
`|vecC|=sqrt((1)/(9)+(4)/(9))=sqrt((5)/(9))`
Hence option (c) is correct.
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