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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class11  >>  3-D Geometry
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Q)

If $P(2,3,4)\;and\:Q(1,b,1)$ are two points and $O$ is origin such that $OP$ is $\perp$ to $OQ$, then $b=?$

$(a)\:\:0\:\:\:\qquad\:\:(b)\:\:2\:\:\:\qquad\:\:(c)\:\:-2\:\:\:\qquad\:\:(d)\:\:No\:real\:value.$

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A)
Given points are $P(2,3,4)\:\:and\:\:Q(1,b,1)$
$\Rightarrow\:\overrightarrow {OP}=(2,3,4)$ and $\overrightarrow {OQ}=(1,b,1)$
Given: $\overrightarrow{OP}$ is $\perp$ to $\overrightarrow {OQ}$
$\Rightarrow\:\overrightarrow{OP}.\overrightarrow {OQ}=0$
$\Rightarrow\:2+3b+4=0\:\:or\:\:b=-2$
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