Which of the following is not a property of vectors?

$A$ unit vector $\vec{a}$ makes an angle $\frac{\pi}{4}$ with the $z$-axis. If $\vec{a} + \hat{i} + \hat{j}$ is a unit vector,then $\vec{a}$ is equal to

Write all the unit vectors in the $XY$-plane.

If $a, b, c$ are any vectors,then the true statement is

Let $\vec{a}, \vec{b},$ and $\vec{c}$ be three non-zero vectors such that no two of them are collinear. If the vector $\vec{a} + 2\vec{b}$ is collinear with $\vec{c}$ and $\vec{b} + 3\vec{c}$ is collinear with $\vec{a}$,then $\vec{a} + 2\vec{b} + 6\vec{c} = \dots$

Let $a = \hat{i} + x \hat{j} + \hat{k}$,$b = \hat{i} + \hat{j} + \hat{k}$ and $|a + b| = |a| + |b|$,then