Unit vectors, vector sums and combinations

Answer Key - Grade 11 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Esme draws u and then v tip to tail on the grid shown. What is the resultant u + v, written as (run, rise)?

   (5, 5)
2. 2.

   Milo draws u and v from one tail on the grid shown and completes the parallelogram. What is u + v, written as (run, rise)?

   (7, 2)
3. 3.

   A boat's motor gives u = ⟨6, 0⟩ km/h and the river adds v = ⟨0, 8⟩. Noah works out the boat's speed. What is |u + v|, in km/h?

   10
4. 4.

   A drone's motors give u = ⟨0, 5⟩ m/s and a breeze adds v = ⟨12, 0⟩. Pia works out the drone's speed. What is |u + v|, in m/s?

   13
5. 5.

   Two ropes pull a cart with u = ⟨4, 3⟩ N and v = ⟨4, -3⟩. Ren works out the size of the total pull. What is |u + v|, in N?

   8
6. 6.

   Two friends tow a sled with u = ⟨8, 6⟩ N and v = ⟨-8, 6⟩. Tala works out the size of the total pull. What is |u + v|, in N?

   12
7. 7.

   Zee has v = ⟨3, 4⟩, whose length is 5. Written as (run, rise), what is the unit vector in the direction of v?

   (3/5, 4/5)
8. 8.

   Esme has v = ⟨-5, 12⟩, whose length is 13. Written as (run, rise), what is the unit vector in the direction of v?

   (-5/13, 12/13)
9. 9.

   Kira has v = ⟨8, -6⟩, whose length is 10. Written as (run, rise), what is the unit vector in the direction of v?

   (4/5, -3/5)
10. 10.

    Luz has v = ⟨-15, -8⟩, whose length is 17. Written as (run, rise), what is the unit vector in the direction of v?

    (-15/17, -8/17)