Vectors in three dimensions

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Milo has u = ⟨1, -2, 3⟩ and v = ⟨2, 1, -1⟩. Written as (x, y, z), what is 2u − 3v?

   (-4, -7, 9)
2. 2.

   Noah has u = ⟨-3, 0, 4⟩ and v = ⟨1, 2, 2⟩. Written as (x, y, z), what is 3u − 2v?

   (-11, -4, 8)
3. 3.

   Pia has u = ⟨2, 5, -1⟩ and v = ⟨-1, 3, 4⟩. Written as (x, y, z), what is 4u − 2v?

   (10, 14, -12)
4. 4.

   A drone climbs 21 m in the direction of d = ⟨2, 3, 6⟩. Tala writes the move as a vector. Written as (x, y, z), what is it?

   (6, 9, 18)
5. 5.

   A diver's camera sinks 27 m in the direction of d = ⟨1, -4, 8⟩. Zee writes the move as a vector. Written as (x, y, z), what is it?

   (3, -12, 24)
6. 6.

   A crane swings a load 22 m in the direction of d = ⟨-2, 6, 9⟩. Esme writes the move as a vector. Written as (x, y, z), what is it?

   (-4, 12, 18)
7. 7.

   A ball rolls down a ramp 18 cm in the direction of d = ⟨4, 4, -7⟩. Jun writes the move as a vector. Written as (x, y, z), what is it?

   (8, 8, -14)
8. 8.

   Kira knows v = ⟨2, y, 6⟩ has length 7 and y is positive. What is y?

   3
9. 9.

   Milo knows v = ⟨6, y, 9⟩ has length 11 and y is positive. What is y?

   2
10. 10.

    Noah knows v = ⟨10, y, 11⟩ has length 15 and y is positive. What is y?

    2