We have, Equation of plane r=b+c+x(a−b)+y(c+a) =(1−x)b+(l+y)c+(x+y)a . . . (i) And equation of line r=a+t(b−c) . . . (ii) From Eqs. (i) and (ii), we have a+t(b−c)=(x+y)a+(1−x)b+(1+y)c ⇒x+y=1 . . . (iii) 1−x=t . . . (iv) 1+y=−t . . . (v) Solving Eqs. (iii), (iv) and (v), we get t=