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# 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 $\alpha=?$

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

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