Add, subtract and scale vectors

Grade 10 Math Worksheet - Building Confidence

Circle the best answer.

1. Read this first

   Use this

   Grid mat. East is the positive run and north is the positive rise. The robot starts at (0, 0), slides u to P, then slides v from P to Q.

2. 1.

   Ari's robot slides u = ⟨4, 1⟩ across the mat, then v = ⟨-1, 3⟩ from where it stopped. Which single slide from the start gives the same finish?

   • ⟨5, -2⟩
   • ⟨3, 4⟩
   • ⟨5, 2⟩
   • ⟨5, 4⟩
3. 2.

   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?

   • 4 km
   • 40 km
   • 8 km
   • 2√10 km, about 6.3 km
4. 3.

   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 west and 4 m north
   • 4 m east and 4 m south
   • 4 m east and 14 m south
5. 4.

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

   • 14 km long, in the opposite direction
   • 10 km long, in the same direction as v
   • 5 km long, in the opposite direction
   • 10 km long, in the opposite direction
6. 5.

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

   • ⟨8, -12⟩
   • ⟨-2, 3⟩
   • ⟨2, -3⟩
   • ⟨2, -6⟩
7. 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?

   • Yes: from stop 2 to stop 3 adds ⟨4, 5⟩, close to the earlier steps
   • Yes: each stop is farther east and north, so the line keeps going
   • Yes: 10 is 5 times 2, so ⟨10, 14⟩ is 5 times ⟨2, 3⟩
   • No: stop 2 is 3 times stop 1, but ⟨10, 14⟩ is not a multiple of ⟨2, 3⟩
8. 7.

   Pia's snail crawls ⟨5, 12⟩ cm. A second crawl goes the same way and is 3 times as long. How long is the second crawl?

   • 51 cm
   • 16 cm
   • 507 cm
   • 39 cm
9. 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, 6⟩
   • ⟨-4, 2⟩
   • ⟨4, -6⟩
   • ⟨-2, 2⟩
10. 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?

    • 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
    • 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
11. 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?

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