A vector B is along positive y-axis and its vector product with...

Given that vector $\vec{B}$ is along the positive y-axis, we can write $\vec{B} = B\hat{j}$ where $B > 0$.

The vector product of $\vec{B}$ and $\vec{A}$ is zero, which means $\vec{B} \times \vec{A} = \vec{0}$.

For the cross product of two non-zero vectors to be zero, the vectors must be parallel or anti-parallel to each other. This implies that $\vec{A}$ must also be directed along the y-axis.

Therefore, $\vec{A}$ must be of the form $A\hat{j}$.

Among the given options, $5\hat{j}$ is the only vector along the y-axis.

Answer: $5\hat{j}$