Question

A vector `vecd` is equally inclined to three vectors `veca=hati-hatj+hatk,vecb=2hati+hatj and vecc=3hatj-2hatk.` Let `vecx,vecy and vecz` be three vectors in the plane of `veca,vecb;vecb,vec;vecc,veca,` respectively. Then
A. `vecz.vecd =0`
B. `vecx.vecd=1`
C. `vecy.vecd= 32`
D. `vecr.vecd= 0 , " where " vecr= lambdavecx+ muvecy+ gammavecz`

Answer 1

Correct Answer - a,d
` veca =hati -hatj +hatk`
` vecb = 2hati +hatj`
`and vecc = 3hatj -2hatk`
since, `[veca vecb vecc]= |{:(1,-1,1),(2,1,0),(0,3,-2):}|=0`
therefore, `veca,vecb and vecc` are coplanar vectors, furthere, sicne `vecd` is equally inclined to `veca, vecb anv vecc` we have
`vecd. veca=vecd.vecb=vecd.vecc=0`
` vecd.vecx=vecd.vecy =vecd.vecz=0`,
`vecd.vecr =0`