The angle between vector $$\vec{Q}$$ and the resultant of $$(2 \vec{Q}+2 \vec{P})$$ and $$(2 \vec{Q}-2 \vec{P})$$ is :

If two vectors $$\vec{A}$$ and $$\vec{B}$$ having equal magnitude $$R$$ are inclined at angle $$\theta$$, then

When vector $$\vec{A}=2 \hat{i}+3 \hat{j}+2 \hat{k}$$ is subtracted from vector $$\overrightarrow{\mathrm{B}}$$, it gives a vector equal to $$2 \hat{j}$$. Then the magnitude of vector $$\overrightarrow{\mathrm{B}}$$ will be :