Can the resultant of three vectors of unequal magnitudes be a zero vector?

The expression $\left( \frac{1}{\sqrt{2}}\hat{i} + \frac{1}{\sqrt{2}}\hat{j} \right)$ is a

The angle made by the vector $(\hat{i} + \hat{j})$ with the $x$-axis and $y$-axis is:

Which of the following colours has the highest energy if the wavelengths of violet, blue, yellow, and red light are $410 \text{ nm}$, $470 \text{ nm}$, $580 \text{ nm}$, and $750 \text{ nm}$ respectively?

Mark the correct statement :-

If $0.5 \hat{i} + 0.8 \hat{j} + c \hat{k}$ is a unit vector, then $c$ is