Three vectors each of magnitude $3 \sqrt{1.5}$ units are acting at a point. If the angle between any two vectors is $\frac{\pi}{3}$, then the magnitude of the resultant vector of the three vector is

A vector perpendicular to the vector $(4 \hat{\mathbf{i}}-3 \hat{\mathbf{j}})$ is

If $\alpha, \beta$ and $\gamma$ are the angles made by a vector with $x, y$ and $z$ axes respectively, then $\sin ^2 \alpha+\sin ^2 \beta=$

If the magnitude of a vector $\mathbf{P}$ is 25 units and its $y$-component is 7 units, then its $x$-component is