How to enter the following two equations in Latex?

Question

How to enter the following two equations in Latex?

Answer 1

I guess there are (at least) two ways to interpret your question:

• mimic the "look" of the screenshot you posted, with its turgid arrow symbols, needlessly oversized delimiter symbols, and unnecessary other symbols (e.g., \times)

• give up on mimicing the screenshot's bloated look and, instead, write down some code that results in a streamlined yet easy-to-read look for both equations.

The following answer tries its hand at both looks. I hope you'll agree that the second look is a whole lot more appealing than the first.

\documentclass{article}
\usepackage{mathtools} % for \DeclarePairedDelimiter macro
\usepackage{old-arrows} % to keep arrow heads from becoming too large
\DeclareMathOperator\argmin{argmin}
\DeclareMathOperator\SEMD{SEM\_D}
\DeclarePairedDelimiter\norm{\lVert}{\rVert}
\begin{document}
bad:
\begin{align*}
&\overrightarrow{t} =
 \mathit{argmin}\biggl( 
 \norm[\Big]{\,\overrightarrow{h} +
               \overrightarrow{e} -
               \overrightarrow{t} }^2\biggr) \\
&\mathit{SEM\_D} \bigl( \,
       \overrightarrow{t_1},
       \overrightarrow{t_2} \bigr)
=\frac{\overrightarrow{t_1}\bullet
       \overrightarrow{t_2}}{%
       \norm[\big]{\,\overrightarrow{t_1}}
       \norm[\big]{\,\overrightarrow{t_2}}}
=\frac{\sum\limits_{i=1}^n 
       \overrightarrow{t_{1i}} \times 
       \overrightarrow{t_{2i}} }{%
       \sqrt{\sum\limits_{i=1}^n
           \bigl(\overrightarrow{t_{1i}}\bigr)^2} \times
       \sqrt{\sum\limits_{i=1}^n
           \bigl(\overrightarrow{t_{2i}}\bigr)^2}}
\end{align*}

\bigskip
good:
\begin{align*}
&\vec{t} =
 \argmin\bigl(\norm{\vec{h} +\vec{e} -\vec{t}\,}^2\bigr) \\
&\SEMD \bigl( \, \vec{t}_1, \vec{t}_2 \bigr)
=\frac{\vec{t}_1\cdot \vec{t}_2}{%
       \norm{\vec{t}_1} \norm{\vec{t}_2}}
=\frac{\sum_{i=1}^n
       \vec{t}_{1i} \, \vec{t}_{2i} }{%
       \sqrt{\sum_{i=1}^n(\vec{t}_{1i})^2} \,
       \sqrt{\sum_{i=1}^n(\vec{t}_{2i})^2}}
\end{align*}
\end{document}