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

The component of vector $\overrightarrow{A}=a_x \hat{i}+a_y \hat{j}+a_z \hat{k}$ along the direction of $\hat{i}-\hat{j}$ is

If the magnitude of a vector $\overrightarrow{p}$ is $25 \text{ units}$ and its $y$-component is $7 \text{ units}$, then its $x$-component is (in $\text{ units}$)

$A$ vector is represented by $3\,\hat i + \hat j + 2\,\hat k$. Its length in the $XY$ plane is

The angles made by the vector $\vec{A} = 2\hat{i} + 3\hat{j}$ with the $x$-axis and the $y$-axis are respectively:

$A$ force is applied at an angle of $60^\circ$ with the horizontal. If its horizontal component is $40 \ N$,then the vertical component is calculated to be ...... $N$.