Three Dimensional Geometry Question 177

Question: The equation of the plane through the origin containing the line $ \frac{x-1}{5}=\frac{y-2}{4}=\frac{z-3}{5} $ is

Options:

A) $ 2x+5y-6z=0 $

B) $ x+5y-5z=0 $

C) $ x-5y+3z=0 $

D) $ x+y-z=0 $

Show Answer

Answer:

Correct Answer: C

Solution:

Trick: A general point $ (5r+1,4r+2,5r+3) $ on the line should satisfy the required plane, which is satisfied by $ x-5y+3z=0. $