# The plane passing through thr points (1,2,1), (2,1,2) and parallel to the line, $2x=3y,z=1$ also passes through the point: Option: 1 $(0,6,-2)$   Option: 2 $(-2,0,1)$ Option: 3 $(0,-6,2)$   Option: 4 $(2,0,-1)$

Two points on the line (L)

$\frac{x}{3}=\frac{y}{2}, z=1 \text { are }(0,0,1)\; \&\;(3,2,1)$

So dr's of the line is ( 3, 2, 0 )

Line passing through (1, 2, 1), parallel to L and coplanar with given plane is

$\overrightarrow{\mathrm{r}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}+\mathrm{t}(3 \hat{\mathrm{i}}+2 \mathrm{j}), \mathrm{t} \in \mathrm{R}(-2,0,1)$ satisfies the line (for t = –1)

(–2, 0, 1) lies on a given plane.

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