A parametric equation of a line between two points P → {\displaystyle {\vec {P}}} and Q → {\displaystyle {\vec {Q}}} is given by ( x , y , z ) = P → + d → t {\displaystyle (x,y,z)={\vec {P}}+{\vec {d}}t} where d → {\displaystyle {\vec {d}}} is the displacement vector. We can compute d → = Q → − P → = ( 2 , − 3 , 12 ) {\displaystyle {\vec {d}}={\vec {Q}}-{\vec {P}}=(2,-3,12)} . It follows that an equation for the line is given by ( x , y , z ) = ( 0 , 5 , 1 ) + ( 2 , − 3 , 12 ) t {\displaystyle (x,y,z)=(0,5,1)+(2,-3,12)t} . Answer: ( x , y , z ) = ( 0 , 5 , 1 ) + ( 2 , − 3 , 12 ) t {\displaystyle \color {blue}(x,y,z)=(0,5,1)+(2,-3,12)t}
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is the displacement vector. 
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