Let:

$$||{\bf u}|| =6$$

$$||{\bf u} + {\bf v}||=6\cdot \sqrt{2}$$

...and let's assume that ${\bf u}$ makes an angle of $45 ^{\circ}$ with a positive $x$-axis, while ${\bf u} + {\bf v}$ makes an angle of $90 ^{\circ}$ with the positive $x$-axis.

What is the component form of ${\bf v}$?