1. [5] Let v1 = and v2 = be two vectors in R4. Determine the linear combination v = 4v1 - 3v2 of these vectors. 2. [8] Determine the scalar (dot) product of the two vectors given in Problem #1. 3. [16] (a) Determine the cross product of the vectors vi Draw a diagram of the vectors and the resultant (you may use a plotting program to do this if you like.) (b) What is the angle between these vectors? 4. [10] Find the unit vector uj in the direction of V1 = [4 5. [12] Determine if the vectors v1 = WNH V2 = , and V3 = are linearly independent. 6. [12] Given the vector v1 = 21 - 5j in the 2D Cartesian plane, where i and j are the unit vectors along the x and y axes respectively, (a) find the equation of the line (in the form y = mx + b) along this vector's directions. (b) If the vector is translated to a starting point of (-2,3), find the equation of the line. 7. [12] Given the vectors vi = | 2 . v2 - 2 . and 03 - [ ] . , determine V1 X V2 . V3 Why would you not do the dot product first here