If |a| , = 3, , ,|b| , = 4 then a value of for which a + b is per… - Vidyadip

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
$\frac{4}{3}$

✓

Answer

Correct option: B.

$\frac{3}{4}$

b
(b) Since $a + \lambda b$ is perpendicular to $a - \lambda b$, then their product will be zero.

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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