Full calculus solutions with good communication are expected!

1. A plane is heading N60 E at 800 km/h. It encounters a wind blowing from $45 E at 75 km/h. Find the resultant velocity of the plane. Include a labeled diagram.2. Determine the equation of the plane in the form Ax + By + Cz + D =0, that passes through the point P(6,-1,1), has z- intercept of -4, and is parallel to the line r = (1, -1,0) + t(2,2, -1) .3. The function f (x) = 2kx' +3x + px -3 has a local minimum at x = -1 and a point of inflection at x =1. Determine the values of k and p.4. The cost of laying power line underwater is 3 times that of underground. An island is 4 km from a straight shoreline at the closest point and a power station is at distance 8 km along the shore from that point. From the power station to the island, how should the power line be laid so that the cost is minimum