SEKOLAH BUKIT SION – HIGH SCHOOL CHAPTER 5: VECTORS

NAME: __________________________________ CLASS: _________ DATE:_____________ 1. Use the diagram below to answer the following.

(a) Write down the column vector of vector a and vector f.

(b) Calculate the magnitude of b and d.

(c) Determine the unit vector of c and e.

2. Given that a = ( !"#) b = ("$% ) and c = ("&"').

(a) Express in column vector of a + 2b – 𝟏

𝟐c.

(b) Find, in simplest forms, the value of r and s if ra + sc = b.

(c) Determine the unit vector of a – b.

3. Points A and B have coordinates (2, –1) and (–3, 3), respectively.

(a) Write 𝐴𝐵#####⃗ as a column vector.

(b) Given that point C is such that 𝐴𝐶#####⃗ = 3𝐴𝐵#####⃗ . Write down the coordinates of C.

4. Use the diagram on the right to answer the questions that follow.

(a) Give the position vectors of points A, C and D.

(b) Using only the points marked red on the

Cartesian plane provided, name: (i) two equal vectors

(ii) two parallel vectors, where k ≠ 1, (iii) two vectors that are of the same magnitude but not of the same direction.

5. Given that 𝐴𝐺######⃗ = a and 𝐴𝐸#####⃗ = b, express the following in terms of a and/or b.

(a) 𝐹𝐶#####⃗

(b) 𝐶𝐻#####⃗

(c) 𝐷𝐵######⃗

(d) 𝐼𝐶####⃗

(e) 𝐺𝐷#####⃗

6. ABCDEF is a regular hexagon.

If 𝐺𝐴#####⃗ = a and 𝐺𝐵#####⃗ = b, express the following in terms of a and/or b.

(a) 𝐹𝐸#####⃗

(b) 𝐴𝐵#####⃗

(c) 𝐶𝐹#####⃗

(d) 𝐸𝐶#####⃗

(e) 𝐴𝐶#####⃗

7. T is the midpoint of the line PS and R divides the line QS in the ratio of 1 : 3.

𝑃𝑇#####⃗ = a and 𝑃𝑄#####⃗ = b.

(a) Express each of the following in terms a and/or b.

(i) 𝑃𝑆####⃗

(ii) 𝑄𝑆#####⃗

(iii) 𝑃𝑅#####⃗

(b) Show that 𝑅𝑇#####⃗ = #$ (2a – 3b).

8. ABC is an isosceles triangle. L is the midpoint of BC.

LM = #%MA and AN = &

'AC.

Given that 𝐵𝐶#####⃗ = p and 𝐵𝐴#####⃗ = q.

(a) Express the following in terms of p and/or q.

(i) 𝐿𝐴#####⃗

(ii) 𝐴𝑁######⃗

(b) Show that 𝑀𝑁#######⃗ = #( (46q – 11p), where t is to be solved.

9. Using the vectors show on the right,

Using appropriate scale on a Cartesian plane, draw the following vectors.

(You may use MS Word/PowerPoint or the softcopy of the graph paper and submit screenshot of your work.)

(a) a + e

(b) -b + 2a

(c) c – d

(d) -c – e

10. In triangle OAB, 𝑂𝐴#####⃗ = a and 𝑂𝐵#####⃗ = b.

P is the point on OA produced such that OP = 3OA.

Q is the point on BP such that PQ = 2QB.

(a) Express the following vectors in terms of a and/or b.

(i) 𝐵𝑃#####⃗

(ii) 𝑄𝐵#####⃗

(iii) 𝐴𝑄#####⃗

(b) Write down the numerical value of:

(i) Area of ∆BAP Area of ∆BOP

(ii) Area of ∆QAP Area of ∆BOP

(iii) Area of ∆OAB Area of ∆BAQ