Forces A and B act at a point. The sum of their magnitudes is 50 N and the magnitude of their resultant is 20 N . If the resultant is at $90^{\circ}$ with the smaller force, the magnitudes of A and B , in N are

If $$\alpha, \beta$$ and $$\gamma$$ are the angles between the vectors $$\overrightarrow{\mathrm{P}}, \overrightarrow{\mathrm{Q}}$$, and $$\overrightarrow{\mathrm{R}}$$ and $$\alpha=90^{\circ}$$ as shown in figure. the product of $$(\vec{Q} \times \vec{R}) \cdot \vec{Q}$$ is equal to

The sides of a parallelogram are represented by vectors $$\vec{p}=5 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$$ and $$\vec{q}=3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$$. Then, the area of the parallelogram is