Question

If the points $(1, 1, \lambda)$ and $( — 3, 0, 1)$ are equidistant from the plane, $3x + 4y —12z + 13 = 0$, then $\lambda$ satisfies the equation :

• A. $3x^2 - 10x + 7 = 0$
• B. $3x^2 + 10x + 7 = 0$
• C. $3x^2 + 10x - 13 = 0$
• D. $3x^2 - 10x + 21 = 0$

Answer 1

Answer: (A)

$\frac{|3+4-12 \lambda+13|}{\sqrt{9+16+144}}=\frac{|-9+0-12+13|}{\sqrt{9+16+144}}$
$\Rightarrow |12 \lambda+20|=|-8|$
$\Rightarrow |-12 \lambda+20|=8$
$\Rightarrow 12 \lambda-20=\pm$
$\Rightarrow 12 \lambda=28$ or 12
$\Rightarrow \lambda=7 / 3$ or
$1 \Rightarrow $ Clearly $3 x^{2}-10 x+7=0$ is satisfied by $\lambda=7 / 3$ and 1