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If vecalpha+ vecbeta+ vecgamma=a vecdel...

If ` vecalpha+ vecbeta+ vecgamma=a vecdeltaa n d vecbeta+ vecgamma+ vecdelta=b vecalpha, vecalphaa n d vecdelta` are non-colliner, then ` vecalpha+ vecbeta+ vecgamma+ vecdelta` equals a. `a vecalpha` b. `b vecdelta` c. `0` d. `(a+b) vecgamma`

A

`a vecalpha `

B

`b vecdelta`

C

`0`

D

`(a+ b)vecgamma`

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Verified by Experts

The correct Answer is:
C
Given `vecalpha + vecbeta + vecgamma = a vecdelta" "` (i)
`" "vecbeta + vecgamma + vecdelta = b vecalpha" "` (ii)
From (i), ` vecalpha + vecbeta + vecdelta = (a+1) vecdelta" "` (iii)
From (ii), `vecalpha + vecbeta + vecgamma + vecdelta = (b+1)vecalpha " "` (iv)
From (iii) and (iv), we get
`" "(a+1) vecdelta = (b+1) vecalpha " "` (v)
Since `vecalpha` is not parallel to `vecdelta`,
From (v), `a=1 =0 and b+1 =0`
From (iii), `vecalpha + vecbeta + vecgamma + vecdelta =0`
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