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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Vector Algebra
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Q)

If $\overrightarrow u=\hat i+\hat j,\:\overrightarrow v=\hat i-\hat j\:and\:\overrightarrow w=\hat i+2\hat j+3\hat k$ and $\overrightarrow n$ is a unit vector such that $\overrightarrow n.\overrightarrow u=\overrightarrow n.\overrightarrow v=0$, then $|\overrightarrow n.\overrightarrow w|=?$

$(a)\:\:o\:\:\:\qquad\:\:(b)\:\:1\:\:\:\qquad\:\:(c)\:\:2\:\:\:\qquad\:\:(d)\:\:3$

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A)
Let $\overrightarrow n=x\hat i+y\hat j+z\hat k$
Given: $ |\overrightarrow n|=1$ $\Rightarrow\: x^2+y^2+z^2=1$........(i)
Given $\overrightarrow u=\hat i+\hat j,\overrightarrow v=\hat i-\hat j\:and\:\overrightarrow w=\hat i+2\hat j+3\hat k$
Also given that $\overrightarrow n.\overrightarrow u=\overrightarrow n.\overrightarrow v=0$
$\Rightarrow\:x+y=0\:\:and\:\:x-y=0$............(ii)
$\Rightarrow\:x=y=0$
Substituting the values of $x\:and\:y$ in (i) we get $z=\pm1$
$\therefore |\overrightarrow n.\overrightarrow w|=3$
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