Add, subtract and scale vectors

Grade 10 Math Worksheet - Building Confidence

Circle the best answer.

1. 1.

   6 km east, then 2 km south. East is the positive run and north is the positive rise. Bo's boat aims ⟨6, 0⟩ km east for an hour while the current pushes it ⟨0, -2⟩ km. How far from the start is the boat after that hour?

   • 40 km
   • 2√10 km, about 6.3 km
   • 8 km
   • 4 km
2. 2.

   Esme's kite drifts u = ⟨-3, 5⟩ m, then v = ⟨7, -9⟩ m. Where does the kite finish compared with where it began?

   • 2 m east and 2 m south
   • 4 m east and 4 m south
   • 4 m east and 14 m south
   • 4 m west and 4 m north
3. 3.

   Jun walks 3 blocks east, then 4 blocks east. A friend walks 3 blocks east, then 4 blocks north. How far from the start does each end?

   • Both end 7 blocks away, since 3 + 4 = 7
   • Jun ends 7 blocks away; the friend ends 25 blocks away
   • Jun ends 5 blocks away; the friend ends 7 blocks away
   • Jun ends 7 blocks away; the friend ends 5 blocks away
4. 4.

   Kira's drone flies v = ⟨3, 4⟩ km. A second flight is -2v. Which describes the second flight's length and direction?

   • 10 km long, in the opposite direction
   • 14 km long, in the opposite direction
   • 5 km long, in the opposite direction
   • 10 km long, in the same direction as v
5. 5.

   Luz's toy rocket moves w = ⟨4, -6⟩ cm on the screen. A half push moves it ½w. Which move is ½w?

   • ⟨2, -6⟩
   • ⟨8, -12⟩
   • ⟨-2, 3⟩
   • ⟨2, -3⟩
6. 6.

   Stops measured from home at the origin. Milo's bike stops are measured from home: stop 1 is ⟨2, 3⟩ km, stop 2 is ⟨6, 9⟩ km. Is stop 3 at ⟨10, 14⟩ km on the same straight line from home?

   • No: stop 2 is 3 times stop 1, but ⟨10, 14⟩ is not a multiple of ⟨2, 3⟩
   • Yes: 10 is 5 times 2, so ⟨10, 14⟩ is 5 times ⟨2, 3⟩
   • Yes: each stop is farther east and north, so the line keeps going
   • Yes: from stop 2 to stop 3 adds ⟨4, 5⟩, close to the earlier steps
7. 7.

   Ren's tent is at A(2, 1) on a map in km and the campfire is at B(7, 4). Which vector is the walk from the tent to the campfire?

   • ⟨5, 3⟩
   • ⟨-5, -3⟩
   • ⟨9, 5⟩
   • ⟨5, -3⟩
8. 8.

   Tala's map shows the school at S(1, -2) and the library at L(-3, 4). Which vector is the route from the school to the library?

   • ⟨-4, 2⟩
   • ⟨-4, 6⟩
   • ⟨-2, 2⟩
   • ⟨4, -6⟩
9. 9.

   Zee's toy car sits at u = ⟨6, 2⟩ at noon and v = ⟨1, 5⟩ at one o'clock, both measured from home. What does v − u tell Zee?

   • Just how many centimeters apart the two spots are, with no direction
   • The total slide if the car first goes to u and then goes v farther
   • The slide that carries the car from its noon spot to its one o'clock spot
   • The slide that carries the car from its one o'clock spot back to its noon spot
10. 10.

    Noah's quilt piece is a parallelogram with sides u = ⟨3, 0⟩ and v = ⟨1, 2⟩ from corner A. Which vector runs from A to the opposite corner C?

    • ⟨4, 2⟩, the sum u + v
    • ⟨-2, 2⟩, the difference v − u
    • ⟨2, -2⟩, the difference u − v
    • ⟨8, 4⟩, twice the sum