JEE Main & Advanced
Mathematics
Three Dimensional Geometry
Question Bank
Critical Thinking
question_answer
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
A)\[{{P}^{2}}-23P+7=0\]
B)\[7{{P}^{2}}-23P+16=0\]
C)\[{{P}^{2}}-17P+16=0\]
D)\[{{P}^{2}}-16P+7=0\]
Correct Answer:
B
Solution :
We have, \[{{P}_{1}}=\left| \,\frac{3\times 2-6\times 3+2\times 4+11}{\sqrt{{{3}^{2}}+{{(-6)}^{2}}+{{(2)}^{2}}}}\, \right|=1\]