<div dir="ltr">I suggest you have a look through this page (<a href="http://mathworld.wolfram.com/VectorAddition.html">http://mathworld.wolfram.com/VectorAddition.html</a>) and the related page linked under "see also" called "vector difference". You can add/subtract two vectors by adding/subtracting the corresponding <b>components</b> (i.e., the u and v components), and making a vector of the resulting sum/difference. What you seem to be stuck on is taking the difference of the <b>magnitude</b> of the vectors rather than the difference of the components.<div>
<br></div><div>I'll use this example to help illustrate this. Suppose you had a westerly wind at 500 mb of 50 kts, and an easterly wind of 50 kts at the surface (unlikely except for possibly within a severe thunderstorm, but just bear with me). There is no difference in the wind speed between 500 mb and the sfc, but there is a difference in the direction. Clearly there is shear, but only if you look at the component form of the wind. The u- and v-components of the 500 mb wind in this example are u = 50, v = 0 (kts), whereas at the surface, the components are u = -50, v = 0 (kts). Therefore, the shear is given by (u500-usfc)<b>i</b> + (v500-vsfc)<b>j</b> = (50 - -50)<b>i</b> + (0-0)<b>j</b> = 100<b>i</b> + 0<b>j</b>. The shear vector is straight out of the west here. The magnitude is given by sqrt(ushear^2 + vshear^2), which is sqrt(100^2 + 0^2) = 100 kts of shear.</div>
<div><br></div><div>Jeff</div></div>