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If veca = (hati + hatj +hatk), veca. vec...

If `veca = (hati + hatj +hatk), veca. vecb= 1 and vecaxxvecb = hatj -hatk , " then " vecb` is (a)`hati - hatj + hatk` (b) `2hati - hatk` (c) `hati` (d) `2hati`

A

3

B

9

C

10

D

12

Text Solution

Verified by Experts

The correct Answer is:
A
Let `vecb=alphahati+betahatj+lambdahatk, veca xx vecb=hatj-hatk`
`rArr |{:(hati,hatj,hatk),(1,1,1),(alpha,beta,lambda):}|=hatj-hatk`
`rArr beta-lambda=0, alpha-lambda=1,alpha-beta=1`
`rArr beta=lambda,alpha=1+lambda,alpha=1+beta`
`veca.vecb=1`
`rArr alpha+beta+lambda=1, rArr beta+1+beta+beta =1 rArr beta=0`
`therefore alpha=1, lambda=0, therefore vecb=hati`
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