Measurement · JHS3 Mathematics

Lesson notes

Learning Objectives

Indicator: B9.3.2.2.2 - Apply the triangular and parallelogram laws of addition to resolve vectors

By the end of the lesson, learners can:

State the triangle law of vector addition in their own words and use it to find the resultant of two vectors placed head-to-tail.
Apply the parallelogram law of vector addition to find the resultant of two vectors placed tail-to-tail.
Express vectors as column vectors and use the triangle law to verify that AB + BC = AC for given points in the Cartesian plane.
Use the parallelogram law to find unknown coordinates of the fourth vertex of a parallelogram given three vertices.
Resolve a given vector into two component vectors along chosen directions to solve practical problems.

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Curriculum details

Strand: Geometry and Measurement (Strand 3)
Sub-strand: Measurement (3.2)
Content standard: B9.3.2.2 - Solve problems involving bearings and addition/subtraction of vectors
Indicator: B9.3.2.2.2 - Apply the triangular and parallelogram laws of addition to resolve vectors
Suggested placement: Term 3, Week 4 (Week 28 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
Curriculum reference: Mathematics, Common Core Programme (JHS1-JHS3), 2023, p. 208
Transcribed from the official NaCCA publication. Check this page against the source.

Exemplars (from the NaCCA curriculum)

E.g.1 Deduce the triangle law of vector addition. ⃗ AB +BC ⃗ = ⃗ AC Where ABC are points in the 0xy plane.
E.g.2 The vertices of a triangle are P(1,-3), Q(7,5) and R(-3,5)
(i) Express PQ, ⃗ ⃗ QR , and PR ⃗ as column vectors.
(ii) Show that triangle PQR is an isosceles.
(iii) Find the equation of the linePR ⃗ .
Eg3 Investigate the parallelogram law of vector addition.
Eg.4P,Q,R,S is a parallelogram whose vertices are P (x ,y), Q (5,7), R(2,4) and S(1,3)
(i) Find PQ, ⃗ andSR ⃗ hence find the values of x and y.