If a unit vector is represented by $\vec{U} = 0.9\hat{i} - 0.2\hat{j} + m\hat{k}$, then the value of $m$ is

The unit vector $(a \hat{\imath} + b \hat{\jmath})$ is perpendicular to $(\hat{\imath} + \hat{\jmath})$. The value of $b$ is

What should be the angle $\theta$ between two vectors $\vec{A}$ and $\vec{B}$ so that the magnitude of the resultant vector $\vec{R}$ is maximum (in $^{\circ}$)?

The angle between the two vectors $\vec A = 3\hat i + 4\hat j + 5\hat k$ and $\vec B = 3\hat i + 4\hat j + 5\hat k$ is ....... $^o$

The resultant magnitude of two vectors of same magnitude is equal to the magnitude of either. The angle between the two vectors is (in $^{\circ}$)

$A$ unit vector does not have any .......