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The condition for equations vec rxx v...

The condition for equations ` vec rxx vec a= vec ba n d vec rxx vec c= vec d` to be consistent is a.` vec b . vec c= vec a . vec d` b. ` vec a . vec b= vec c .vec d` c. ` vec b . vec c+ vec a . vec d=0` d. ` vec adot vec b+ vec cdot vec d=0`

A

`vecb.vecc=veca.vecd`

B

`veca.vecb=vecc.vecd`

C

`vecb.vecc+veca.vecd=0`

D

`veca.vecb+vecc.vecd=0`

Text Solution

Verified by Experts

The correct Answer is:
c
` vecr xx veca = vecb `
` or vecd xx ( vecr xx veca)= vecd xx vecb`
`or (veca .vecd) vecr - (vecd.vecr) veca= vecd xx vecb`
` vecr xx vecc = vecd`
` or vecb xx ( vecr xx vecc) = vecb xx vecd`
` or (vecb .vecc) vecr - (vecb.vecr) vecc = vecb xx vecd`
Adding (i) and (ii) , we get
` ( veca. vecd + vecb . vecc) vecr- (vecd.vecr) veca - (vecb.vecr) vecc `
Now `vecr.vecd = 0 and vecb.vecr=0 as vecd and vecr` as `vecb and vecr` are mutually perpendicular.
Hence ` ( vecb.vecc + veca.vecd)vecr = vec0`
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