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For what value of \( \lambda \) are the vectors \( \overrightarrow a = 2\hat i - \lambda \hat j + \hat k\: and \: \overrightarrow b = \hat i - 2\hat j + 3\hat k\) perpendicular to each other?

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  • If two vectors are $\perp$ then $\overrightarrow a.\overrightarrow b=0$
$\overrightarrow a=\hat i-\lambda \hat j+\hat k$
$\overrightarrow b=\hat i-2 \hat j+3\hat k$
If two vectors are $\perp$ then $\overrightarrow a.\overrightarrow b=0$
$(\hat i-\lambda \hat j+\hat k).(\hat i-2 \hat j+3\hat k)=0$
$\Rightarrow 2+2\lambda+3=0$
$\Rightarrow 2\lambda+5=0$
$\Rightarrow 2\lambda=-5$
$\lambda=\large\frac{-5}{2}$
answered Sep 26, 2013 by sreemathi.v
 

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