MCQ
If $|a|\, = 3,\,\,|b|\, = 4$ then a value of $\lambda$ for which $a + \lambda b$ is perpendicular to $a - \lambda b$ is
- A$\frac{9}{16}$
- ✓$\frac{3}{4}$
- C$\frac{3}{2}$
- D$\frac{4}{3}$
So, $(a + \lambda b).(a - \lambda b) = 0$ ==> $|a{|^2} - {\lambda ^2}|b{|^2} = 0$
or ${\lambda ^2} = \frac{{|a{|^2}}}{{|b{|^2}}} \Rightarrow {\lambda ^2} = \frac{9}{{16}}$ or $\lambda = \pm \frac{3}{4}$,
$[\because \,|a| = 3,|b| = 4]$
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If A and B are events such that
$\text{P}(\text{A}|\text{B})=\text{P}(\text{B}|\text{A}),\ \text{then}:$