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

• A. $P^2-23P+7=0$
• B. $7P^2-23P+16=0$
• C. $P^2-17P+16=0$
• D. $P^2-16P+7=0$

Answer 1

The correct option is B $7P^2-23P+16=0$

We have, $P_1=\left|\frac{3\times 2-6\times 3+2\times 4+11}{\sqrt{3^2+(-6{)}^2+(2{)}^2}}\right|=1$
$P_2=\left|\frac{3\times 1-6\times 1+2\times 4+11}{\sqrt{3^2+(-6{)}^2+(2{)}^2}}\right|=\frac{16}{7}$
So, equation whose roots are $P_1$ and $P_2$ is,
$7P^2-23P+16=0$.