Three Dimensional Geometry Question 412
Question: If $ P_1 $ and $ P_2 $ are the lengths of the perpendiculars from the points (2,3,4) and (1,1,4) respectively from the plane $ 3x-6y+2z+11=0 $ , then $ P_1 $ and $ P_2 $ are the roots of the equation
Options:
A) $ P^{2}-23P+7=0 $
B) $ 7P^{2}-23P+16=0 $
C) $ P^{2}-17P+16=0 $
D) $ P^{2}-16P+7=0 $
Show Answer
Answer:
Correct Answer: B
Solution:
We have, $ P_1=| ,\frac{3\times 2-6\times 3+2\times 4+11}{\sqrt{3^{2}+{{(-6)}^{2}}+{{(2)}^{2}}}}, |=1 $
$ P_2=| \frac{3\times 1-6\times 1+2\times 4+11}{\sqrt{3^{2}+{{(-6)}^{2}}+{{(2)}^{2}}}} |=\frac{16}{7} $
So, equation whose roots are $ P_1 $ and $ P_2 $ is,
$ 7P^{2}-23P+16=0 $ .
BETA
