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Question Number 23442 by chernoaguero@gmail.com last updated on 30/Oct/17

$$\mathrm{Find}\mathrm{a}\mathrm{unit}\mathrm{vector}\mathrm{which}\mathrm{is}\mathrm{perpendicula}$$$$\mathrm{to}\mathrm{a}\mathrm{vector}\mathrm{A}\left(3\mathrm{coma}5\mathrm{coma}1\right)$$$$$$$$\mathrm{Sorry}\mathrm{for}\mathrm{writing}\mathrm{coma}\mathrm{cuz}\mathrm{i}\mathrm{dnt}\mathrm{see}\mathrm{a}\mathrm{key}\mathrm{for}\mathrm{it}$$

Commented by $@ty@m last updated on 31/Oct/17

Commented by chernoaguero@gmail.com last updated on 31/Oct/17

$$\mathrm{oopz}\mathrm{u}\mathrm{are}\mathrm{right}\mathrm{i}\mathrm{was}\mathrm{seachin}\mathrm{for}\mathrm{it}$$$$\mathrm{since}\mathrm{but}\mathrm{could}\mathrm{not}\mathrm{see}\mathrm{iti}$$

Answered by $@ty@m last updated on 31/Oct/17

$$Given,$$$$\overrightarrow{OA}=3\hat{i}+5\hat{j}+\hat{k}$$$$Let\overrightarrow{OB}=x\hat{i}+y\hat{j}+z\hat{k}suchthat$$$$\overrightarrow{OA}\mathrm{\perp }\overrightarrow{OB}\mathrm{\&}\mid OB\mid =1....\left(1\right)$$$$\Rightarrow \overrightarrow{OA}.\overrightarrow{OB}=0$$$$\Rightarrow 3x+5y+z=0....\left(2\right)$$$$Therewouldbeinfiniteunit$$$$vectors\overrightarrow{OB}=x\hat{i}+y\hat{j}+z\hat{k}$$$$satisfyingconditions\left(1\right)and\left(2\right).$$$$Forexample,$$$$Letx=0$$$$then{y}^2+z^2=1\mathrm{\&}5y+z=0$$$$\Rightarrow y=\pm \frac{\sqrt{26}}{26}\mathrm{\&}z=\mp \frac{5\sqrt{26}}{26}$$$$\therefore oneofthepossibleunitvectors$$$$perpendicularto\overrightarrow{OA}is$$$$\frac{\sqrt{26}}{26}\hat{j}-\frac{5\sqrt{26}}{26}\hat{k}$$

Commented by chernoaguero@gmail.com last updated on 01/Nov/17

$$\mathrm{Thank}\mathrm{u}\mathrm{so}\mathrm{much}$$

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