Please help me out with this question. I tried to study but keep hitting dead end. Thank you very much.

1. Consider the vectors a = (k, 0, 0) and b = (0, /, 0). Find all unit vectors, c, such that the angle between a and c is it/3 while the angle between b and c is 31/4. 2. Use vector cross product to derive a formula for the area of a triangle with vertices (X,. Yo. Zo). (x1. )1. 21), (x2, 2.Z2) in terms of only the coordinates of the three vertices. 3. Let a, b # 0 be vectors in R with angle between them 1/7, and c = a x b. Find the angle between each pair of vectors: c and b c and b x a b and b x c a and b x c q x c and b x c