A vector $\vec{A}$ points vertically upward and $\vec{B}$ points towards north. The vector product \[\vec{A}\times \vec{B}\] is: -
A. null vector
B. along west
C. along east
D. vertically downward

Hint: Use the proper hand rule for determination of the direction of the resulting vector and therefore the definition of the magnitude (for the resultant) for the cross-product’s size. You might be ready to use your imagination to urge the direction by thinking of a globe and where the vectors $A\And B$ are pointing. confirm you understand what the angle between $A\And B$

Formula used:
Cross product between two vectors:
$\vec{A}\times \vec{B}=A\cdot B\cdot \sin \Phi $
Where:
$\Phi $- angle between two vectors

Complete step by step answer:
Cross product: The notation is $\vec{A}\times \vec{B}$
 and therefore the results a vector with magnitude
$\Rightarrow A\cdot B\cdot \sin \Phi $
 where $\Phi $is the angle between vectors.
If you would like the vector product of your $2$ vectors, the results a vector with magnitude
$\Rightarrow A\cdot B$ note that $\sin \left( {{90}^{\circ }} \right)=1$
For determination of the vector requires the use of the right-hand-rule. Open your right palm far away from you and point the fingers up, the direction of vector $\vec{A}$ Face north and curl your fingers to horizontal, the direction of vector $\vec{B}$. Extend your thumb which will be West. Therefore, the vector product points West.

So, the correct answer is “Option B”.

Additional Information:
Vectors are quantities that are fully described by both a magnitude and a direction. For vector quantity usually, an arrow is employed on the highest like $\vec{v}$ which represents the vector value of the speed and also explains that the number has both magnitudes also as direction.

Note:
The addition and subtraction of vector quantities doesn't follow the straightforward arithmetic rules. A special set of rules are followed for the addition and subtraction of vectors. Here are some points to be noted while adding vectors: Addition of vectors means finding the resultant variety of vectors working on a body. The component vectors whose resultant is to be calculated are independent of every other. Each vector acts as if the opposite vectors were absent. Vectors are often added geometrically but not algebraically.