Three Dimensional Geometry Question 14
Question: Chord AB is a diameter of the sphere $ | \vec{r}-2\vec{i}-\vec{j}+6\vec{k} |=\sqrt{18.} $ if the coordinates of A are (3, 2,-2), then the coordinates of B are
Options:
A) (1, 0, 10)
B) (1, 0, -10)
C) (-1, 0, 10)
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
The equation of the sphere is $ | r-2\vec{i}-\vec{j}+6\vec{k} |=\sqrt{18} $
$ \Rightarrow $ Its centre is at the point $ (\vec{r}-2\vec{i}-\vec{j}+6\vec{k}) $ , i.e, at $ (2,1,-6). $ coordinates of A are $ (3,2,-2) $ . Let the coordinates of B be $ (\alpha ,\beta ,\gamma ) $ . Then, $ \frac{3+\alpha }{2}=2,\frac{2+\beta }{2}=1 $ and $ \frac{-2+\lambda }{2}=-6 $
$ \Rightarrow \alpha =1,\beta =0,\lambda =-10 $ Therefore, coordinates of B are $ (1,0,-10). $
BETA
