Physics - Vectors Question with Solution | TestHub

$$\begin{array}{l}\hat{\mathrm{n}}=a\hat{\mathrm{i}}+b\hat{\mathrm{j}}\\ \overrightarrow{\mathrm{r}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}\end{array}$$ If $\hat{n}$ is perpendicular to the vector $\vec{r}=\hat{i}+\hat{j}$ $\hat{n}\cdot \vec{r}=0$ $a+b=0$ $b=-a.\dots ..(1)$ The magnitude of unity vector is $1.$ $\sqrt{a^2+b^2}=1$ $\sqrt{a^2+a^2}=\sqrt{2}a=1($ from equation 1) $a=\frac{1}{\sqrt{2}}$ $a=\frac{1}{\sqrt{2}}$ and from equation (1), we get $b=-\frac{1}{\sqrt{2}}$ The correct option is D.