Vectors: magnitude, direction and component form

Answer Key - Grade 10 Math Worksheet - Challenge Me

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

1. 1.

   Noah's kite string is a vector of length 12 units at 35° counterclockwise from the positive x-axis. To the nearest tenth, what is it in component form, as (run, rise)?

   (9.8, 6.9)
2. 2.

   Pia's rocket flight path is a vector of length 10 units at 58° counterclockwise from the positive x-axis. To the nearest tenth, what is it in component form, as (run, rise)?

   (5.3, 8.5)
3. 3.

   Ren's robot arm is a vector of length 15 units at 133° counterclockwise from the positive x-axis. To the nearest tenth, what is it in component form, as (run, rise)?

   (-10.2, 11.0)
4. 4.

   Tala's boat drift is a vector of length 10 units at 219° counterclockwise from the positive x-axis. To the nearest tenth, what is it in component form, as (run, rise)?

   (-7.8, -6.3)
5. 5.

   A gust blows Bo's kite at 16 km/h on a bearing of S 26° E. To the nearest tenth, what is the velocity in component form, as (east, north), in km/h?

   (7.0, -14.4)
6. 6.

   Esme bikes at 24 km/h on a bearing of S 50° W. To the nearest tenth, what is the velocity in component form, as (east, north), in km/h?

   (-18.4, -15.4)
7. 7.

   Jun's robot slides straight from P(-2, 3) to Q(4, -1) on a map in kilometers. What is the length of vector PQ, as a simplified radical or whole number?

   2√13
8. 8.

   Kira's drone slides straight from P(5, -6) to Q(-1, 2) on a map in kilometers. What is the length of vector PQ, as a simplified radical or whole number?

   10
9. 9.

   Luz's scooter slides straight from P(-4, -7) to Q(2, 5) on a map in kilometers. What is the length of vector PQ, as a simplified radical or whole number?

   6√5
10. 10.

    Milo's boat slides straight from P(3, 8) to Q(-4, 1) on a map in kilometers. What is the length of vector PQ, as a simplified radical or whole number?

    7√2