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The diagram below shows two vectors u,v such that lies in the positive quadrant of the xy-plane (meaning the x and y coordinates are both positive) and ||u|| =2 and ||v|| lies on the positive portion of the z -axis and ||v||=3.  If $$\mathbf u\times\mathbf v = \begin{pmatrix} a\\b\\c \end{pmatrix},$$ what is the sign of a and what is $$\|\mathbf u\times\mathbf v\|?$$

May 2, 2020