Hello, I need help with these grade 12 university level calculus and vector math questions, please. For a good review please be detailed and thorough when answering the questions. And please answer all the questions correctly too :) Thank you !

Introduction to Vectors 1. Which of these physical quantities is a vector and which is a scalar? a. the mass ofthe moon b. the acceleration of a drag racer c. the velocity of a wave at the beach d. the speed of light e. the force of gravity f. the magnetic field of the earth g. the area of a rectangle h. the temperature of a swimming pool 2. ABCDEF is a regular hexagon. Give an example of vectors which are 9' equal b. parallel but having different magnitudes c. equal in magnitude but opposite in direction d. equal in magnitude but not equal vectors e. different in both magnitude and direction 3. Determine the magnitude and direction of each of the vectors below. Assume up is north, right is east, down is south, left is west. 4. Examine the vectors in the diagram above. Express d and 5" each as a scalar multiple of E. 5. A search and rescue aircraft, travelling at a speed of 160 km/h, starts out at a heading of N 35 W. After travelling for one hour and fifteen minutes, it turns to a heading of N 80 E and continues for another 2 hours before returning to base. a. Determine the displacement vector for each leg of the trip. b. Find the total distance the aircraft travelled and how long it took. 6. If a = 5 meters north, and b= 10 meters S 70 E , a. Calculate the vector 2a - 3b (including magnitude and direction) b. Determine the unit vector in the same direction as 2a - 3b7- In the diagram, ABCDEFGH is a regular octagon (recall: a regular octagon has > all sides equal length and all angles equal measure), as shown below. Let AB = 3 > _. and AH = (3. Since these vectors are not collinear, they form a basis for the plane, and all other vectors in the plane can be expressed as linear combinations of Ii and s 4} 4) 4} 6. Express the vectors along the other sides of the octagon ( BC, CD, DE, . . .) as a sum of scalar multiples of E, and 3