Please solve 4,5,6,7 and Challenge section in details and fully explanation.

4. If's and t are unit vectors, and s + t) = V3, determine(25 - 5t) . (35 + t). 5. Determine the value(s) of k such that the area of the parallelogram formed by the vectors a = (k + 1, 1, - 2)and b = (k, 3, 0) is V41. 6. A hammock is tied between two trees that are 6m apart. One rope is 4 metres long and the other rope is 5m. The ropes have a rating of 700N. Will the ropes support a person with a mass of 100kg? Assume that 1 kg exerts a force of 9.8 N 7. Parallelogram OBCA has its sides determined by OA = a = (4, 2, 4) and OB = b = (3, 1, 4). Its fourth vertex is point C. A line is drawn from B perpendicular to side ACof the parallelogram to intersect AC atN. Determine the length of BN. CHALLENGE: You, a civil engineer and contractor, are building a new monument for the city. The monument will take the shape of an equilateral tetrahedron, as it marks a breakthrough on clean methane fracking. Each side of the monument is an equilateral triangle. Three different perspectives of the model are pictured below. (Hint: You will receive more bonus marks by applying vector concepts.) What is the angle of elevation, observed from one of its base vertices to the top