# 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 $\alpha=?$

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

If a line lies on a plane then every point of the line satisfies the equation of the plane.
A point on the given line is $(4,2,\alpha)$
This point satisfies the eqn. of the plane $2x-4y+z=7$
$\therefore 8-8+\alpha=7$
$\Rightarrow\:\alpha=7$