Answer
Perpendicular
Work Step by Step
$x+4y-3=1$ and $-3x+6y+7z=0$
Since the dot product of the two vectors is equal to zero, they are perpendicular.
$n_1=\lt1,4,-3\gt$ and $n_2=\lt -3,6,7\gt$
$n_1 \cdot n_2=\lt1,4,-3\gt \cdot \lt -3,6,7\gt$
$n_1 \cdot n_2=-3+24-21$
$n_1 \cdot n_2=0$
Hence, the planes are perpendicular.
