Given two vectors $\overrightarrow{\mathrm{A}}=3\hat{\mathrm{i}}+4\hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{B}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$. $\mathrm{\theta }$ is the angle between $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$. Which of the following statements is/are correct?

Component of $\overrightarrow{\mathrm{A}}$ along $\overrightarrow{\mathrm{B}}$ is $\left|\overrightarrow{\mathrm{A}}\right|\cos \mathrm{\theta }\hat{\mathrm{B}}$ for $\mathrm{\theta }$ being the angle between the vectors.

Also $\widehat{\mathrm{B}}=\frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}}$. So choice (1) is correct.

The vector $( \hat{\mathrm{i}}-\hat{\mathrm{j}} )$ is perpendicular to the vector $( \hat{\mathrm{i}}+\hat{\mathrm{j}} )$.

So the other resolved component is $\left|\overrightarrow{\mathrm{A}}\right|\sin \mathrm{\theta }\left(\frac{\hat{\mathrm{i}}-\hat{\mathrm{j}}}{\sqrt{2}}\right)$