Three Dimensional Geometry Question 304
Question: If the distance of the point (1, 1,1) from the origin is half its distance from the plane $ x+y+z+k=0 $ , then $ k= $
[Kerala (Engg.)2005]
Options:
A) $ \pm 3 $
B) $ \pm 6 $
C) ?3, 9
D) $ 3,,-9 $
Show Answer
Answer:
Correct Answer: D
Solution:
Distance of the point (1,1,1) from origin $ =\sqrt{{{(1)}^{2}}+{{(1)}^{2}}+{{(1)}^{2}}}=\sqrt{3} $ Distance of the point (1,1,1) from $ x+y+z+k=0 $ is, $ \pm \frac{(1)+(1)+(1)+k}{\sqrt{{{(1)}^{2}}+{{(1)}^{2}}+{{(1)}^{2}}}}=\pm \frac{k+3}{\sqrt{3}} $ According to question, $ \sqrt{3}=\pm \frac{1}{2}( \frac{k+3}{\sqrt{3}} ) $
Þ $ 6=\pm (k+3) $
Þ $ k=3,-9 $ . 3, 9
BETA
