Add, subtract and scale vectors

Grade 10 Math Worksheet

Circle the best answer.

1. 1.

   Three ropes pull Ari's sled with u = ⟨12, 0⟩, v = ⟨0, 5⟩ and w = ⟨-6, 3⟩ newtons. How hard do they pull in total, the length of u + v + w?

   • About 23.7 N
   • 10 N
   • About 18.1 N
   • 17 N
2. 2.

   Their directions are not given. Esme rides two legs of 7 km and 4 km, in any directions. Which statement describes how far from the start the finish can be?

   • Exactly 3 km, because 7 − 4 = 3
   • Anywhere from 0 km to 11 km
   • Anywhere from 3 km to 11 km
   • Exactly 11 km, because 7 + 4 = 11
3. 3.

   Luz's drone A flies from A(1, -2) to B(7, 6). A second drone leaves C(-4, 3) and flies twice that slide. Where does the second drone stop?

   • (8, 19)
   • (2, 11)
   • (-16, -13)
   • (8, 11)
4. 4.

   Pia's robot map is a parallelogram ABCD with A(1, 1), B(5, 2) and C(8, 6) in order around it. Where is corner D?

   • (4, 5)
   • (-2, -3)
   • (12, 7)
   • (9, 7)
5. 5.

   Ren places a beacon halfway between sensors P(-2, 6) and Q(10, -4). Which position is right, and how is it found?

   • (6, -5), from ½(Q − P)
   • (8, 2), from P + Q
   • (4, 1), from P + ½(Q − P)
   • (22, -14), from P + 2(Q − P)
6. 6.

   Short string ⟨8, 15⟩ m, length 17 m. The long string has the same direction and is 51 m long. Milo's kite string runs ⟨8, 15⟩ m (17 m long). A longer string must be 51 m long in the same direction. Which vector is the longer string?

   • ⟨-24, -45⟩
   • ⟨24, 45⟩
   • ⟨408, 765⟩
   • ⟨42, 49⟩
7. 7.

   The lists give |u|, |v| and |u + v|. Vectors u and v have lengths 5 and 9. Tala lists possible lengths for u, v and u + v. Which list cannot happen?

   • 5, 9 and 4
   • 5, 9 and 14
   • 5, 9 and 15
   • 5, 9 and 10
8. 8.

   Zee's scooter makes slide A = 3⟨2, -1⟩ and slide B = ⟨8, -4⟩. How do A and B compare?

   • B points the same way as A and is 4 times as long
   • B points the same way as A and is 2 units longer in the run
   • B points the same way as A and is 4/3 as long
   • B points opposite to A, since its parts are 8 and -4
9. 9.

   Kira swims at 5 km/h in still water. The current pushes ⟨3, 0⟩ km/h. Kira wants the total velocity to point straight north. Which swim vector works?

   • ⟨0, 5⟩
   • ⟨-3, 5⟩
   • ⟨3, 4⟩
   • ⟨-3, 4⟩
10. 10.

    Esme's rug border is a loop of four slides: u = ⟨4, 3⟩, v = ⟨-1, 5⟩, w, and x = ⟨-6, -2⟩. The loop ends where it began. What is w?

    • ⟨-9, -10⟩
    • ⟨-3, 6⟩
    • ⟨3, -6⟩
    • ⟨3, 6⟩