Vectors in three dimensions

Answer Key - Grade 11 Math Worksheet

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

1. 1.

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

   (3, 1, 3)
2. 2.

   Milo has u = ⟨7, 1, -3⟩ and v = ⟨-2, 5, -6⟩. Written as (x, y, z), what is u − v?

   (9, -4, 3)
3. 3.

   Noah has u = ⟨0, -4, 8⟩ and v = ⟨5, -1, 3⟩. Written as (x, y, z), what is u − v?

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

   Pia needs the unit vector in the direction of v = ⟨2, -3, 6⟩. Written as (x, y, z) with fractions, what is it?

   (2/7, -3/7, 6/7)
5. 5.

   Ren needs the unit vector in the direction of v = ⟨-4, 4, 7⟩. Written as (x, y, z) with fractions, what is it?

   (-4/9, 4/9, 7/9)
6. 6.

   Tala needs the unit vector in the direction of v = ⟨1, -8, -4⟩. Written as (x, y, z) with fractions, what is it?

   (1/9, -8/9, -4/9)
7. 7.

   Zee needs the unit vector in the direction of v = ⟨-6, 2, -9⟩. Written as (x, y, z) with fractions, what is it?

   (-6/11, 2/11, -9/11)
8. 8.

   A drone flies straight from point (2, 1, 0) to (4, 4, 6), in meters. Esme finds the straight-line distance. How many meters is it?

   7
9. 9.

   A robot arm moves a block from (-1, 3, 0) to (7, -1, 1), in meters. Kira finds the straight-line distance. How many meters is it?

   9
10. 10.

    A balloon rises from (0, -2, 4) to (9, 4, 6), in meters. Luz finds the straight-line distance. How many meters is it?

    11