The equation of the plane passing through the points (2, -1, 0), (3, -4, 5) and parallel to the line 2x = 3y = 4z is :
Answer & explanation
Correct answer: option 4
Give line is 2x = 3y = 4z
i.e., $\frac{x}{6}=\frac{y}{4}=\frac{z}{3}$
Let the plane be
Ax + by + cz = 1
We have
6a + 4b + 3c = 0
2a – b = 1
3a – 4b + 5c = 1
$\Rightarrow a=\frac{29}{85}, b=\frac{27}{85}, c=-\frac{22}{85}$
Thus equation of plane is
29x – 27y – 22z = 85