Find the vector equation of a line passing through the origin and perpendicular to the plane r ?.(i ?+2j ?+3k ? )=3 The answer given in the book is: r ?=?(i ?-2j ?+3k ? ),where ? is a scalar .

Equation needs to be perpendicular to the given plane. The vector perpendicular to the plane is (i+2j+3k ) and hence the line perpendicular to the plane would be parallel to this normal vector. So, the direction ratios of line are given by 1,2,3 and lien passes through (0,0,0)

Hence, x/1 =y/2 = z/3 = t

x = t, y = 2t, z = 3t

Hence, equation of line r = xi + yj+zk = t(i+2j+3k)

The answer in the book is wrong. It should be 2j and not -2j.