v1 = initial velocity
v2 = final velocity
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Delta "T"=V2-V1 ---- A
1. If V1 and V2 be two vectors at 900 from each other, having magnitudes of 10 and 20 units each, what will be the value of V1.V2 ?
Yes, a unit vector can have negative component since a unit vector has same magnitude and direction as a negative unit vector. Here is the general work out of the problem: Let |v| be the norm of (v1, v2). Then, the unit vector is (v1/|v|, v2/|v|). Determine the "modulus" or the norm |(v1/|v|, v2/|v|)| to get 1, which is the new norm. If we determine the norm of |(-v1/|v|, -v2/|v|)|, we still have the same norm 1.
Calculate percentage changefrom V1 = 3624 to V2 = 8236[ ((V2 - V1) / |V1|) * 100 ]= ((8236 - 3624) / |3624|) * 100= (4612 / 3624) * 100= 1.272627 * 100= 127.2627% change= 127.26% increase.
A Compound Graph is an extension of a standard graph. Let G be a graph, G=(V,E) where V is a set of vertices and E is a set of edges, that is e = (v1, v2) in V2 A compound graph C is defined by a tree T=(V,F) where V is the same set as G and F are tree edges f=(v1,v2) in V2. C=(G,T) where G=(V,E) and T=(V,F) Furthermore, C has two additional constraints: e=(v1,v2) in E implies: 1) v1 is not on the path of v2 to the root of T AND 2) v2 is not on the path of v1 to the root of T. Intuitively, T defines a hierarchy. All the vertices sharing the same parent in T are in the same "group". The constraints state that you cannot have an edge connecting a vertex to one of its parent in the hierarchy.