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If veca , vecb and vecc are three vecto...

If `veca , vecb and vecc ` are three vectors such that `vecaxx vecb =vecc, vecb xx vecc= veca, vecc xx veca =vecb` then prove that `|veca|= |vecb|=|vecc|`

A

`vecA = ((vecaxxvecb)-veca)/(a^(2))`

B

`vecB = ((vecbxx veca) + veca (a^(2) - 1))/a^(2)`

C

`vecA = ((vecaxxvecb)+veca)/(a^(2))`

D

`vecB = ((vecbxx veca) - veca (a^(2) - 1))/a^(2)`

Text Solution

Verified by Experts

The correct Answer is:
b,c,
we have `vecA.vecB =veca`
`or vecA .veca + vecB.veca = veca.veca`
`or 1+ vecB.veca = a^(2)`
`or vecB.veca= a^(2)-1`
Also `vecA xx vecB =vecb`
`or veca xx (vecA xx vecB ) = veca xx vecb`
` or (veca. vecB)vecA - (veca.vecA) vecB = veca xx vecb`
`or (a^(2)-1) vecA -vecB = veca xx vecb`
( using (i) and ` veca. vecA =1`) (ii)
` and vecA + vecB =a`
form (ii) and (iii) , we have
`vecA= ((vecaxxvecb)+veca)/a^(2)`
`vecB=veca-{((vecaxxvecb)+veca)/a^(2)}`
` = ((vecbxxveca) + veca (a^(2) -1))/a^(2)`
thus `vecA= ((vecaxxvecb)+veca)/a^(2)`
` and vecB= ((vecbxxveca)+veca (a^(2) -1))/a^(2)`
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