1. Captain Crunch wants his airplane to travel along a path that is [?60?] with a groundspeed of 280 km/h. If the wind is blowing from the direction [?10?] at 65 km/h, then in what direction should the pilot steer towards and what would be his airspeed? Include a labelled diagram. Use the COMPONENT method.2. According to Kanye East (not to be confused with Kanye West), (?? ?) ?? = ?? (? ?? ). Is this world renowned rapper correct? Justify your answer by providing an example.3. Given the vectors ? = (?1,?2,?3) and ?=(?1,?2,?3) show that ? ? = ?? ?.4. The angle between two vectors ? = (1, 1, 2) and ? = (?1, 2, ?) is 60. Find the value(s) of k.5. |?| = 11, |?| = 23 , and |? ? ?| = 30, determine the length of ? + ?. Include a diagram as a part of your solution.6. State the components of a unit vector that is perpendicular to the vector ? = (5, 2, ?1).

l. A 6 kg sign is suspended by two strings making angles with the ceiling as shown in the diagram. Determine the magnitudes of the tensions in each string. Remember that 1kg exerts a force of 9.8 N. Use SINEICOSINE LAW for this question. 48 67