What is the maximum number of components into which a vector can be resolved?

If $\vec{A} = \hat{i} A \cos \theta + \hat{j} A \sin \theta$ is a vector,then another vector $\vec{B}$ which is perpendicular to $\vec{A}$ is given by:

Three vectors $\overrightarrow{OP}, \overrightarrow{OQ}$ and $\overrightarrow{OR}$ each of magnitude $A$ are acting as shown in the figure. The resultant of the three vectors is $A \sqrt{x}$. The value of $x$ is:

The projection of a vector $\vec{r} = 3\hat{i} + \hat{j} + 2\hat{k}$ on the $xy$-plane has magnitude:

$A$ force of $5\, N$ acts on a particle along a direction making an angle of $60^\circ$ with the vertical. Its vertical component is.......$N$.

The $y$-component of vector $\vec{A}$ is $+3.0 \ m$. If $\vec{A}$ makes an angle of $30^{\circ}$ counterclockwise from the positive $y$-axis,the magnitude of $\vec{A}$ is (assume $\vec{A}$ is in the $x-y$ plane).