A vector ` vec d` is equally inclined to three vectors ` vec a= hat i+ hat j+ hat k , vec b=2 hat i+ hat ja n d vec c=3 hat j-2 hat kdot` Let` vec x , vec y ,a n d vec z` be three vectors in the plane of ` vec a , vec b ; vec b , vec c ; vec c , vec a ,` respectively. Then a.` vec x. vec d=-1` b. ` vec y. vec d=1` c. ` vec z. vec d=0` d. ` vec r. vec d=0,w h e r e vec r=lambda vec x+mu vec y+delta vec z`

Options

A. `vecx.vecd=-1`
B. `vecy.vecd= 1`
C. vecz.vecd=0`
D. vecr.vecd=0, " where " vecr=lambda vecx + mu vecy +deltavecz`

Answer

c.d

Explanation

Since `[veca vecb vecc] =0, veca, vecb and vecc` are coplanar vectors.
Further, since, `vecd` is equally inclined to `veca ,vecb and vecc,`
`vecd.veca =vecd.vecb = vecd.vecc=0`
`vecd.vecx =vecd.vecy = vecd.vecz =0`
`vecd.vecr =0`