$$ r(t)=\langle 3+3t,-5,7+t\rangle.$$
Work Step by Step
The vector parametrization of the line is given by $$ r(t)=(3,-5,7)+t\langle 3,0,1\rangle, $$ that is $$ r(t)=\langle 3+3t,-5,7+t\rangle.$$
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