Three Dimensional Geometry Question 30
Question: Co-ordinate of a point equidistant from the points (0,0,0), (a, 0, 0), (0, b, 0), (0, 0, c) is
[RPET 2003]
Options:
A) $ ( \frac{a}{4},\frac{b}{4},\frac{c}{4} ) $
B) $ ( \frac{a}{2},\frac{b}{4},\frac{c}{4} ) $
C) $ ( \frac{a}{2},\frac{b}{2},\frac{c}{2} ) $
D) (a, b, c)
Show Answer
Answer:
Correct Answer: C
Solution:
The required point is the centre of the sphere through the given points. Let the equation of sphere be $ x^{2}+y^{2}+2ux+2vy+2wz+d=0 $ …..(i) Sphere (i) is passing through (0, 0, 0), (a, 0, 0), (0, b, 0) and (0, 0, c),
$ \therefore d=0 $ $ a^{2}+2ua=0\Rightarrow u=-a/2 $ $ b^{2}+2vb=0\Rightarrow v=-b/2 $ $ c^{2}+2wc=0,\Rightarrow w=-c/2 $ Therefore, centre of sphere is $ (a/2,,b/2,,c/2) $ , which is also the required point.
BETA
