Any triangle can be represented by three vectors u, v, w. 1) Make a sketch of...

 

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Any triangle can be represented by three vectors u, v, w. 1) Make a sketch of an example triangle with the tails of u and at the same point and w pointing from the head of 7 to the head of u. 2) Find an equation for win terms of u and 7. 3) Use the equation to find a relationship between the squared lengths of u, v, w, where the squared length of a vector is u² = |u|² = u. ū. Use the relation between the dot product and angle between two vectors to recover the Law of Cosines. 4) Show that the area of the triangle A = |ū × v|/2. Prove the other cross products give the same result A = |uxw|/2 = w × v| /2. Any triangle can be represented by three vectors u, v, w. 1) Make a sketch of an example triangle with the tails of u and at the same point and w pointing from the head of 7 to the head of u. 2) Find an equation for win terms of u and 7. 3) Use the equation to find a relationship between the squared lengths of u, v, w, where the squared length of a vector is u² = |u|² = u. ū. Use the relation between the dot product and angle between two vectors to recover the Law of Cosines. 4) Show that the area of the triangle A = |ū × v|/2. Prove the other cross products give the same result A = |uxw|/2 = w × v| /2.