The line $\overrightarrow r=(4\hat i+2\hat j+\alpha \hat k)+\lambda(\hat i+\hat j+2\hat k)$ lies on the plane $2x-4y+z=7$ if $\alpha=?$

Question

$(a)\:\:7\:\:\:\:\qquad\:\:(b)\:\:-7\:\:\:\:\qquad\:\:(c)\:\:1\:\:\:\:\qquad\:\:(d)\:\:0$.