GMNG 4310 Lab 2 Solve the following problems. You must show steps to receive full credit. (1) Let v1 = (5, −1, 4) and v2 = (4, 3, 1). Find (i) the length of (v1 + v2). (ii) the angle between v1 and v2. (iii) v1 · v2. (iv) v1 · (v2 × v1) (2) Suppose we have a triangle with three vertices in the order of V0, V1 and V2. The three vertices are represented by three vectors V0 = (1, −2, 3) V1 = (0, 1, 1) V2 = (1, 0, 2). Find the unit normal vector of this triangle. (3) Let A =   −1 3 1 2 4 −1 −1 −1 0   and B =   2 1 0 1 −3 1 −2 −1 3   , Find (i) AB. (ii) BA. (4) A point P in a plane has coordinates x = 5.7, y = −3.6. Now we rotate the axes 120◦ counterclockwise to become x 0 and y 0 . Find the new coordinates (x 0 , y0 ) of this point P. (5) Let q1 = 1 + 2i − j + k and q2 = 1 − i + j − k be two quaternions. (i) Find q 2 1 . (ii) Find q 2 2 . (iii) Find q1q2. (iv) Find q2q1. 1

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