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, k, 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 3x/4. 2. Use vector cross product to derive a formula for the area of a triangle with vertices (X,. yo. Z,). (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 a x c and b x c 4. Given two parallel planes ax + by + cz = d and ax + by + cz = e, derive a formula for the distance between them. 5. Consider the elliptical path c(t) = (;cost, 2 sint ). Find the coordinates of the points on the curve where the curvature is minimum and maximum. Recall: k (() = '(x"( where 7(t) is the unit tangent vector to c(t) at time t. You may use a different formula if you know It