A unit vector in the direction of resultant vector of $\overrightarrow{\mathrm{A}}=-2\widehat{\mathrm{i}}+3\widehat{\mathrm{j}}+\widehat{\mathrm{k}}\mathrm{and}\overrightarrow{\mathrm{B}}=\widehat{\mathrm{i}}+2\widehat{\mathrm{j}}-4\widehat{\mathrm{k}}\mathrm{is}$

Here, $\overrightarrow{\mathrm{A}}=-2\widehat{\mathrm{i}}+3\widehat{\mathrm{j}}+\widehat{\mathrm{k}}$

$\overrightarrow{\mathrm{B}}=\widehat{\mathrm{i}}+2\widehat{\mathrm{j}}-4\widehat{\mathrm{k}}$

The resultant vector of $\overrightarrow{\mathrm{A}}\mathrm{and}\overrightarrow{\mathrm{B}}$ is

$\overrightarrow{\mathrm{R}}=\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}=(2\widehat{\mathrm{i}}+3\widehat{\mathrm{j}}+\widehat{\mathrm{k}})+(\widehat{\mathrm{i}}+2\widehat{\mathrm{j}}-4\widehat{\mathrm{k}})$

$=-\widehat{\mathrm{i}}+5\widehat{\mathrm{j}}-3\widehat{\mathrm{k}}$

$\left|\overrightarrow{\mathrm{R}}\right|=\sqrt{{(-1)}^2+{\left(5\right)}^2+{(-3)}^2}\text{= }\sqrt{1+25+9}\text{ = }\sqrt{35}$

Unit vector in the direction of resultant vector of $\overrightarrow{\mathrm{A}}\mathrm{and}\overrightarrow{\mathrm{B}}$ is

$\widehat{\mathrm{R}}=\frac{\overrightarrow{\mathrm{R}}}{\left|\overrightarrow{\mathrm{R}}\right|}=\frac{-\widehat{\mathrm{i}}+5\widehat{\mathrm{j}}-3\widehat{\mathrm{k}}}{\sqrt{35}}$