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Question Number 194218 by Mingma last updated on 30/Jun/23

Commented by Frix last updated on 30/Jun/23

$$t=-\frac{3}{2}$$

Commented by Mingma last updated on 30/Jun/23

Good!

Answered by cortano12 last updated on 01/Jul/23

$$\Rightarrow \overrightarrow{a}+\mathrm{t}\overrightarrow{b}=\left(\begin{array}{c}1+\mathrm{t}\\ 2+\mathrm{t}\\ 3+2\mathrm{t}\end{array}\right)$$$$\Rightarrow \mid \overrightarrow{a}+\mathrm{t}\overrightarrow{b}\mid =\sqrt{{(1+\mathrm{t})}^2+{(2+\mathrm{t})}^2+{(3+2\mathrm{t})}^2}$$$$\mathrm{let}\mathrm{f}\left(\mathrm{t}\right)={\mathrm{t}}^2+2\mathrm{t}+1+{\mathrm{t}}^2+4\mathrm{t}+4+{4\mathrm{t}}^2+12\mathrm{t}+9$$$$\mathrm{f}\left(\mathrm{t}\right)={6\mathrm{t}}^2+18\mathrm{t}+14$$$$\mathrm{f}{\left(\mathrm{t}\right)}_{\min }\mathrm{when}\mathrm{t}=-\frac{18}{12}=-\frac{3}{2}$$$$\underset{―}{}$$

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