Data analysis

To find the domain of the vector valued function.

Given vector function,

\(\displaystyle{r}{\left({t}\right)}={\frac{{{2}}}{{{t}-{1}}}}{i}+{\frac{{{3}}}{{{t}+{2}}}}{j}\)

Domain of vector function

The domain of a vector function is the values of vector function parameter for which the components of vector function are defined.

Here, 't' is the function parameter and coefficients of i and j are the components.

Horizontal component is defined if,

\(\displaystyle{\frac{{{2}}}{{{\left({t}-{1}\right)}}}}\) is defined for all the values of 't' in real excluding \(\displaystyle{t}={1}\).

As when \(\displaystyle{t}={1}\), component (\(\displaystyle{\frac{{{1}}}{{{2}}}}\)) which is undefined.

Vertical component is defined if,

\(\displaystyle{\frac{{{3}}}{{{\left({t}+{2}\right)}}}}\) is defined for all the values of 't' in real excluding \(\displaystyle{t}=-{2}\).

As when \(\displaystyle{t}=-{2}\), component \(\displaystyle={\frac{{{3}}}{{{0}}}}\) which is undefined.

Hence, Domain of \(r\left(t\right)=\left\{t\mid R-\left\{-2, 1\right\}\right\}\)

Where R is real numbers.