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# If the position vector of the points $A\:and\:B$ are $\hat i-\hat j+3\hat k$ and $3\hat i+3\hat j+3\hat k$ and the equation of a plane is $\overrightarrow r.(5\hat i+2\hat j-7\hat k)+9=0$, then the points $A\:and\:B$ are?

$\begin{array}{1 1} (a)\:lie\: on\: the\: plane.\:\qquad\:(b)\:are\: on\: the\: same\:side\:of\:the\:plane.\:\qquad\:(c)\:are\:on\:opp.\:sides\:of\:the\:plane.\:\qquad\:(d)\:none\:of\:these \end{array}$

Here the equation of the plane in cartesian form is $5x+2y-7z+9=0$ and
the points are $A(1,-1,3)\:\:and\:\:B(3,3,3)$
Substituting the coordinates of $A$ and $B$ on the equation of the plane,
$A$ gives $-ve$ sign and $B$ gives $+ve$ sign.
$\therefore$ They lie on opposite sides of the plane.