MATH 32A Study Guide - Final Guide: Row And Column Vectors, Unit Vector, Quadrilateral
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In class during week 2, we saw that kv k = kv ewk. (this is easy to prove. ) However, this only gives the magnitude of v , not the actual vector v . Find a formula, using only cross products, for the vector v , and explain/prove why the formula works: show that for any quadrilateral p qrs, its area can be computed as (cid:13)(cid:13)(cid:13) (cid:13)(cid:13)(cid:13) . In other words, the area of any quadrilateral is equal to one half the magnitude of the cross product of its two diagonals. Note: be sure to show that this is still correct when the quadrilateral is not convex, such as in the second case shown below. In problem 48 in section 13. 4 (from homework 3), you showed the same thing for cross products: if a v = a w and a 6= 0, then you cannot cancel out the a and conclude that v = w.
