Vectors: magnitude, direction and component form

Answer Key - Grade 10 Math Worksheet

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

1. 1.

   A model plane flies straight from P to Q over Noah's map. P is (-2, 5) and Q is (4, -3). What is vector PQ in component form, written as (run, rise)?

   (6, -8)
2. 2.

   Ren's kite moves from P to Q in a gust. P is (-7, -1) and Q is (-2, 9). What is vector PQ in component form, written as (run, rise)?

   (5, 10)
3. 3.

   Zee's drone makes the slide v = ⟨4, -6⟩ in meters. What is the length of v, as a simplified radical?

   2√13
4. 4.

   Ari's kite makes the slide v = ⟨-3, 9⟩ in meters. What is the length of v, as a simplified radical?

   3√10
5. 5.

   Bo's robot makes the slide v = ⟨-8, -4⟩ in meters. What is the length of v, as a simplified radical?

   4√5
6. 6.

   Esme's boat makes the slide v = ⟨10, 5⟩ in meters. What is the length of v, as a simplified radical?

   5√5
7. 7.

   Jun's kite moves along v = ⟨5, 3⟩. To the nearest degree, what is its direction angle, measured counterclockwise from the positive x-axis?

   31
8. 8.

   Kira's rocket moves along v = ⟨2, 7⟩. To the nearest degree, what is its direction angle, measured counterclockwise from the positive x-axis?

   74
9. 9.

   Luz's boat moves along v = ⟨-4, 3⟩. To the nearest degree, what is its direction angle, measured counterclockwise from the positive x-axis?

   143
10. 10.

    Milo's airplane moves along v = ⟨6, -5⟩. To the nearest degree, what is its direction angle, measured counterclockwise from the positive x-axis?

    320