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Question Number 115793 by ZiYangLee last updated on 28/Sep/20

$$\mathrm{Given}\mathrm{that}\underset{\backsim }{p}=\left(\begin{array}{c}2\\ -3\end{array}\right),\underset{\backsim }{q}=\left(\begin{array}{c}-4\\ m\end{array}\right)\mathrm{and}\underset{\backsim }{r}=\left(\begin{array}{c}n\\ 4\end{array}\right)$$$$\mathrm{If}\underset{\backsim }{p}+\underset{\backsim }{q}-\underset{\backsim }{r}\mathrm{is}\mathrm{a}\mathrm{unit}\mathrm{vector},\mathrm{find}\mathrm{the}\mathrm{value}$$$$\mathrm{of}m\mathrm{and}n.$$

Answered by $@y@m last updated on 29/Sep/20

$$p=2i-3j$$$$q=-4i+mj$$$$r=ni+4j$$$$p+q-r=(2-4-n)i+(-3+m-4)j$$$$=(-2-n)i+(m-7)j$$$$\because p+q-r\mathrm{is}\mathrm{a}\mathrm{unit}\mathrm{vector}.$$$$\therefore \mid p+q-r\mid =1$$$$\Rightarrow {(-2-n)}^2+{(m-7)}^2=1...\left(A\right)$$$$Infinitevaluesarepossibleform,n$$$$satisfying\left(A\right)$$

Commented by ZiYangLee last updated on 29/Sep/20

$$\mathrm{Hmmm}...$$

Commented by ZiYangLee last updated on 05/Oct/20

$$\mathrm{you}\mathrm{are}\mathrm{right}$$

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