If the line drawn from the point (-2, -3, -4) meets a plane at right angle at the point (1, -2, 4), then equation of plane is :

3x + y + 8z -33 = 0

The correct answer is Option (1) → $3x + y + 8z -33 = 0$

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

$\vec n=(\hat i-2\hat j+4\hat k)-(-2\hat i-3\hat j-4\hat k)$

$\vec n=3\hat i+\hat j+8\hat k$

So equation → $(\vec r-\vec a).\vec n=0$

$⇒\vec r-\vec n=\vec a.\vec n$

$3x+y+8z=3-2+32$

$3x+y+8z-33=0$