(Solved): Determine the vector equation of each line. a) parallel to the \( x \)-axis a ...

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Determine the vector equation of each line. a) parallel to the \( x \)-axis and through \( \mathrm{P}_{0}(3,-8) \) b) perpendicular to \( 4 x-3 y=17 \) and through \( \mathrm{P}_{0}(-2,4) \) c) with the same \( x \)-intercept as \( [x, y, z]=[3,0,0]+t[4,-4,1] \) and the same z-intercept as \[ [x, y, z]=[6,-2,-3]+t[3,-1,-2] \]