1. Consider the cube ABCDEFGH with the side length equal to 10cm . Find the magnitude of the following vectors: a) AB b) BD C) BH H G E F D C B 2. Prove or disprove each statement. a) If a =b then | a Hb|- b) If | a | =b | then a =b . 3. Two vectors are defined by a =4M[E] and b =5/[0909]. Find the sum vector s =a + b the difference vector d =a-b . 4. Two vectors are defined by a = 2km[W] and b = 4km[S]. Find the sum vector $ =a + b the difference vector d= a-b . 5. Two vectors are defined by a = 20m[E] and b =30m[1509] - Find the sum vector $ =a + b the difference vector d=a-b. 6. Given a = 27 -37 +k , b =-7 + ] + 2k , simplify the following expressions: a) a +b b) a - 2b c) 2a -3b 7. Find a unit vector parallel to the sum between a = 2m(E] and b = 3m[N]- 8. Given u = 8m(W] and v =10m($30-W/], determine the magnitude and the direction of the vector 24 - 3v . 9. Adam can swim at the rate of 2km / h in still water. At what angle to the bank of a river must he head if he wants to swim directly across the river and the current in the river moves at the rate of Ikm/ h ? 10. A plane is heading due north with an air speed of 400km/h when it is blown off course by a wind of 100km / h from the northeast. Determine the resultant ground velocity of the airplane (magnitude and direction). 11. A car is travelling at Ver = 100km/ #[E], a motorcycle is travelling at Vman = 80km/ A[W/] , a truck is travelling at "wwe = 120km / /[N] and an SUV is travelling at Vse =100km / h[SHI/]. Find the relative velocity of the car relative to: a) motorcycle truck c) SUV