Cartesian equation of plane passing through the points (2, -4, 5) and perpendicular to the line with direction ratios (3, -1, 2) is :

$3x-y + 2z =20$

The correct answer is option (2) → $3x-y + 2z =20$

point $\vec a=2\hat i-4\hat j+5\hat k$

$\vec n=3\hat i-\hat j+2\hat k$

$(\vec r-\vec a).\vec n=0⇒\vec r.\vec n=\vec a.\vec n$

$⇒3x-y+2z=6+4+10$

$⇒3x-y+2z=20$