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

enter image source here

1 Answer
Sep 6, 2017

C will have the smallest X product.


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:
#AXB = |A|*|B|*sin(gamma)#
where #gamma# is the angle between A and B. #gamma# is to be measured in the direction which yields a measurement between #0^@# and #180^@#.

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^@#. 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^@# or #180^@#:
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,