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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
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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