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?

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

   • Jun ends 7 blocks away; the friend ends 25 blocks away
   • Both end 7 blocks away, since 3 + 4 = 7
   • Jun ends 5 blocks away; the friend ends 7 blocks away
   • Jun ends 7 blocks away; the friend ends 5 blocks away
5. 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
   • 10 km long, in the same direction as v
   • 5 km long, in the opposite direction
   • 14 km long, in the opposite direction
6. 5.

   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: 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
7. 6.

   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?

   • 16 cm
   • 51 cm
   • 39 cm
   • 507 cm
8. 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⟩
   • ⟨5, -3⟩
   • ⟨9, 5⟩
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⟩
   • ⟨-2, 2⟩
   • ⟨-4, 2⟩
   • ⟨-4, 6⟩
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?

    • 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
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?

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