Mathematics - Vector Question with Solution | TestHub

Let $\overrightarrow{\mathrm{u}}=\hat{\mathrm{i}}+\hat{\mathrm{j}},\overrightarrow{\mathrm{v}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{w}}=\hat{\mathrm{i}}+2\hat{\mathrm{j}}+3\hat{\mathrm{k}}$. If $\hat{\mathrm{n}}$ is a unit vector such that $\vec{u}\cdot \hat{n}=0$ and $\overrightarrow{\mathrm{v}}\cdot \hat{\mathrm{n}}=0$, then $|\overrightarrow{\mathrm{w}}\cdot \hat{\mathrm{n}}|$ is equal to