Let a = (1,2, 1), c = (3, 1, -5) and d = (3, 1, 5)....

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Let a = (1,2, 1), c = (3, 1, -5) and d = (3, 1, 5). (a) Without trying to write out the components of the cross product, why do you know that there are no vectors v so that a x v = d? (b) Without trying to write out the components of the cross product, how do you know there are no unit vectors v so that a x v = c? (c) Find a vector v 1a so that a x v = c. How many such v can there be? Why? (d) Let v be as in (c). Take any vector b so that a x (v + b) = c. What could b possibly be? Let a = (1,2, 1), c = (3, 1, -5) and d = (3, 1, 5). (a) Without trying to write out the components of the cross product, why do you know that there are no vectors v so that a x v = d? (b) Without trying to write out the components of the cross product, how do you know there are no unit vectors v so that a x v = c? (c) Find a vector v 1a so that a x v = c. How many such v can there be? Why? (d) Let v be as in (c). Take any vector b so that a x (v + b) = c. What could b possibly be?