The value of $k$ for which the line $\overrightarrow r=(4\hat i+2\hat j-\hat k)+\lambda(\hat i-k\hat j+2\hat k)$ lies on the plane $2x-4y+z=3$ is ?

Question

$(a)\;1\qquad(b)\;-1\qquad(c)\;No\;real\;value\;of\;k\qquad(d)\;3$