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If veca is any non-zero vector, then (ve...

If `veca` is any non-zero vector, then `(veca.hati)hati+(veca.hatj)hatj+(veca.veck)hatk` is equal to …….

A

`vecr`

B

` 2vecr`

C

`3vecr`

D

`vec0`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `vecr= x hati + y hat j + zhatk` be an arbitrary vector. Then ,
` vecr.hati = ( x hati + yhatj + zhatk) .hati =x ( hati .hati) +y (hatj .hati) +z (hatk .hati) =x`
` vecr.hatj = ( xhati + yhatj + zhatk) .hatk= x ( hati .hatk)+ y (hatj .hatk) +z (hatk .hatk)`
and ` vecr.hatk = ( xhati +yhatj +zhatk).hatk= x ( hati.hatk) + y (hatj.hatk) +z (hatk.hatk) `
Putting the values of x,y,z in `vecr = xhati + yhatj + zhatk ` . we obtain
`vecr= ( vecr.hati) hati +( vecr.hatj) hatj+ ( vecr. hatk) hatk`
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