Consider the following three (candidate) state vectors: a) normalize each of the above states (following our convention that the coefficient of the +> basis ket is always positive and real.) b) for each ofthese three states, find the probability that the spin component will be "up" along the z-direction. use bra-ket notation in your calculations! c) for just the second state, 2〉, find the probability that the spin component will be "up" along the x-direction. use bra-ket notation in your calculations. (hint: you will need mclntyre 1.33 for this one. you will need mclntyre 1.60 for the next d) for just state iva〉, find the probability that the spin component will be "up" along the y-direction. use braket notation in your calculations. be careful, there is some slightly nasty complex-number arithmetic required on this one that is very important, and frequently people make mistakes on it that turn out to really change the answer significantly!