Three Dimensional Geometry Question 188
Question: If P be the point (2, 6, 3), then the equation of the plane through P at right angle to OP, O being the origin, is
[MP PET 2000; Pb. CET 2001]
Options:
A) $ 2x+6y+3z=7 $
B) $ 2x-6y+3z=7 $
C) $ 2x+6y-3z=49 $
D) $ 2x+6y+3z=49 $
Show Answer
Answer:
Correct Answer: D
Solution:
Distance of point P from origin $ OP=\sqrt{4+36+9}=7 $ Now d.r?s of OP = 2?0, 6 ? 0, 3 ? 0 = 2, 6, 3 \ d.c?s of OP = $ \frac{2}{7},,\frac{6}{7},,\frac{3}{7} $ \Equation of plane in normal form is $ lx+my+nz=p $
Þ $ \frac{2}{7}x+\frac{6}{7}y+\frac{3}{7}z=7 $
Þ $ 2x+6y+3z=49 $ .
BETA
