The condition for equations `vecrxxveca = vecb and vecr xx vecc = vecd` to be consistent is

Options

A. `vecb.vecc=veca.vecd`
B. `veca.vecb=vecc.vecd`
C. `vecb.vecc+veca.vecd=0`
D. `veca.vecb+vecc.vecd=0`

Answer

c

Explanation

` 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`