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1. Suppose a = (a1, (2, a3) and b = (b1, 62, 63) are two arbitrary vectors. Compute their the triple product of a, b, and a (in that order) and simplify your solution as much as possible. (Hint: use the triple product formula u . (v x w ) for the three vectors u, v, w. ) 2. True or False: If a, b are two arbitrary vectors then a | b = all + bl. Briefly justify your answer. 3. True or False: If a, b are two arbitrary vectors then a x b| = b x all. Briefly justify your answer. 4. Two lines in the ry plane either intersect at a single point or are parallel. a) When you have two lines in 3d space (so ryz space), what are the possibilities? b) What about two planes in 3d space? c) What about three planes in 3d space? d) Or four planes in 3d space? e) What about a line and a plane in 3d space? 5. What is the line of intersection between the azz and yz planes? Write a vector equation and a standard parametrization