ALEX Learning Activity Resources

   View Standards     Standard(s): [MA2019] PRE-19 (9-12) 12 :

12. Add and subtract vectors.

a. Add vectors end-to-end, component-wise, and by the parallelogram rule, understanding that the magnitude of a sum of two vectors is not always the sum of the magnitudes.

b. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

c. Explain vector subtraction, v - w, as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

In this learning activity, students will learn to add or subtract two vectors. The activity will teach the students that they simply add or subtract their components. In other words, add the x component of the first vector to the x component of the second and so on for y and z. The answers the students will get from adding or subtracting the x, y, and z components of their original vectors are the x, y, and z components of their new vector. This learning activity should be used as an introductory activity. Corresponding activities can be found in the Notes or Recommendations section.

   View Standards     Standard(s): [MA2019] PRE-19 (9-12) 12 :

12. Add and subtract vectors.

a. Add vectors end-to-end, component-wise, and by the parallelogram rule, understanding that the magnitude of a sum of two vectors is not always the sum of the magnitudes.

b. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

c. Explain vector subtraction, v - w, as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

In this learning activity, students will learn to add or subtract two vectors. The activity will teach the students how to add and subtract vectors in 2D. Vectors can be represented by line segments with a specific length (magnitude) and directions. Students will use this information to help visualize vector addition and subtraction. The scope of this learning activity will only consider vectors in two dimensions; however, the methodology described can be extended to vectors in three or more dimensions. The teacher will recall that a unit vector is a vector with a magnitude equal to 1 and that the unit vectors in the 𝑥- and 𝑦-directions are denoted by  ⃑𝑖 and ⃑𝑗 respectively. This learning activity can be used as a core lesson activity. Corresponding activities can be found in the Notes or Recommendations section.

   View Standards     Standard(s): [MA2019] PRE-19 (9-12) 12 :

12. Add and subtract vectors.

a. Add vectors end-to-end, component-wise, and by the parallelogram rule, understanding that the magnitude of a sum of two vectors is not always the sum of the magnitudes.

b. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

c. Explain vector subtraction, v - w, as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

In this learning activity, students will practice adding and subtracting vectors in 2D. This learning activity can be used as a stand-alone activity or an assessment activity for the corresponding activities found in the Notes or Recommendations section.