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.

   Pia's toy boat drifts straight from P to Q on a pond map. P is (3, -4) and Q is (-5, 2). What is vector PQ in component form, written as (run, rise)?

   (-8, 6)
3. 3.

   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)
4. 4.

   Tala bikes straight from P to Q on a town map. P is (6, 2) and Q is (-3, -5). What is vector PQ in component form, written as (run, rise)?

   (-9, -7)
5. 5.

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

   2√13
6. 6.

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

   3√10
7. 7.

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

   5√5
8. 8.

   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
9. 9.

   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
10. 10.

    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