Vectors in three dimensions

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

   A drone flies from its pad along v = ⟨2, 3, 6⟩ m, with x east, y north and z up. Esme finds how far that is. What is |v|, in m?

   7
2. 2.

   A kite's string runs from the spool along v = ⟨1, 4, -8⟩ m, with x east, y north and z up. Jun finds how far that is. What is |v|, in m?

   9
3. 3.

   A crane moves a load along v = ⟨-2, 6, 9⟩ m, with x east, y north and z up. Kira finds how far that is. What is |v|, in m?

   11
4. 4.

   Milo draws an arrow from P(1, 2, -1) to Q(4, -2, 3). Written as (x, y, z), what is the component form of the arrow from P to Q?

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

   Noah draws an arrow from P(0, 5, 2) to Q(3, 1, 7). Written as (x, y, z), what is the component form of the arrow from P to Q?

   (3, -4, 5)
6. 6.

   Pia draws an arrow from P(-2, 4, 6) to Q(1, 4, -3). Written as (x, y, z), what is the component form of the arrow from P to Q?

   (3, 0, -9)
7. 7.

   Ren draws an arrow from P(5, -1, 0) to Q(2, 3, -4). Written as (x, y, z), what is the component form of the arrow from P to Q?

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

   A robot repeats the move v = ⟨2, -1, 4⟩, scaled by 3. Tala writes 3v. Written as (x, y, z), what is 3v?

   (6, -3, 12)
9. 9.

   A drone reverses the move v = ⟨1, 5, -3⟩, scaled by -2. Zee writes -2v. Written as (x, y, z), what is -2v?

   (-2, -10, 6)
10. 10.

    A game piece repeats the jump v = ⟨-3, 0, 2⟩, scaled by 4. Esme writes 4v. Written as (x, y, z), what is 4v?

    (-12, 0, 8)