# Which of the following pairs of vectors will have the smallest cross product? Not sure how to do this.

Sep 6, 2017

C will have the smallest X product.

#### Explanation:

To me the most straight-forward way to explain cross product of 2 vectors is to say it is the product of the magnitude of the 2 vectors multiplied by the sine of the angle between the vectors. Written as an equation:
$A X B = | A | \cdot | B | \cdot \sin \left(\gamma\right)$
where $\gamma$ is the angle between A and B. $\gamma$ is to be measured in the direction which yields a measurement between ${0}^{\circ}$ and ${180}^{\circ}$.

This simple explanation is not suitable in all situations. But it definitely applies well to this question. The angle $\gamma$ in option C appears to be ${180}^{\circ}$. Since the sine of "180^@ is zero, C yields the smallest result of the 4.

An example of a case in which the angle between the vectors is either ${0}^{\circ}$ or ${180}^{\circ}$:
Place a socket wrench on a nut. Push on, or pull on, the handle of the socket wrench so that the push or pull is along the shaft of the handle of the wrench - pushing toward the nut or pulling away from the nut. Operation of a wrench generates torque best when the direction of the force is perpendicular to the length of the handle of the wrench.

I hope this helps,
Steve