Three Dimensional Geometry Question 7
Question: If O, P are the points (0, 0, 0), (2, 3, -1) respectively, then what is the equation to the plane through P at right angles to OP?
Options:
A) $ 2x+3y+z=16 $
B) $ 2x+3y-z=14 $
C) $ 2x+3y+z=14 $
D) $ 2x+3y-z=0 $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Since, coordinates of points O and P are (0, 0, 0) and (2, 3, -1), respectively. Direction ratios of OP are <2, 3, -1>. The plane is perpendicular to OP, so, its equation is $ 2x+3y-z+d=0 $ (i) Since, this plane passes through $ (2,3-1);2\times 2+3\times 3-1\times -1+d=0 $
$ \Rightarrow 4+9+1+d=0 $
$ \Rightarrow d=-14 $ On putting the value of d in equation (i) $ 2x+3y-z-14=0 $
$ \Rightarrow 2x+3y-z=14 $ Which is required equation of plane.
BETA
