Consider the vector 13 in the diagram below (the diagram uses bold font to denote a vector]. You will be drawing vectors on this diagram. 1. Using its three Cartesian projections, labelled in the diagram, write the vector a. as a 1x3 column matrix and b. in terms of the unit vectors. 5,], E, (these are the unit vectors along the x, y, and 2 directions) 2. Consider if 13 = PUP-F"??? {"7 1 1 1 Calculate t3 - E by multiplying the vectors component by component. Calculate the vector lengths, i.e., ll and [El Calculate the angle 6' between 13 and H using \"E3 - E = Il Il cos 3 Draw E and the length 13 - H along it, in the diagram [trace or copy it} Calculate 13 + H. Now roughly draw the resulting vector by drawing 13 and E tip to tail. Show that all the vectors F that satisfy equation, 173 - F = 0 are perpendicular to 1?. Sketch the plane that is defined by (Le, made up of) this set of vectors, F. .Another vector is E 2 (153+ 0.5} + U E, 3. In this part, you will calculate cross products. El. b. For the unit vectors, 3. X} = E. What is E X j equal to? What is] X 3 equal to? What is E X j' equal to? For the same vectors as in part 2, calculate the vector that results from 13 x E. Draw in the diagram the vector in part b