MCQ
If the line passes through the points $P(6,-1,2)$, $Q(8,-7,2 \lambda)$ and $R(5,2,4)$ then value of $\lambda$ is
- A
- B
- C$x+2 y+2 z=6, x+2 y+2 z=0$
- D$x-2 y+2 z=0 . x-2 y+2 z-6=0$
(d) : Equation of any plane parallel to the plane
$x-2 y+2 z+4=0 \text { is } x-2 y+2 z+\lambda=0 \text {. }$
Its distance from the point $(1,2,3)$ is 1 unit.
$\begin{aligned}
& \therefore \frac{|1-2(2)+2(3)+\lambda|}{\sqrt{1^2+(-2)^2+(2)^2}}=1 \Rightarrow \frac{|1-4+6+\lambda|}{3} \\
& \Rightarrow|3+\lambda|=3 \\
& \Rightarrow 3+\lambda= \pm 3 \Rightarrow \lambda=0,-6
\end{aligned}$
$\therefore$ Equations of planes are
$x-2 y+2 z=0 \text { and } x-2 y+2 z-6=0$
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The p.d.f. of a c.r.v. $X$ is
$ f(x)=\left\{\begin{array}{c} 6 x(1-x), \quad 0 \leq x \leq 1 \\ 0, \quad \text { elsewhere } \end{array}\right. $
If $P(X<a)=P(X>a)$, then $a=$