Cambridge International Mathematics

ef 2 Find a single vector which is equal to: a ¡! QR+ ¡! RS b ¡! PQ+ ¡! QR c ¡! PS+ ¡! SR+ ¡! RQ d ¡! PR+ ¡! RQ+ ¡! QS 3 Paolo r ...

Example 6 Self Tutor For points P, Q, R and S, simplify the following vector expressions: a ¡! QR¡ ¡! SR b ¡! QR¡ ¡! SR¡ ¡! PS a ...

de f 2 For points P, Q, R and S, simplify the following vector expressions: a ¡! QR+ ¡! RS b ¡! PS¡ ¡! RS c ¡! RS+ ¡! SR d ¡! RS ...

An alternative to plotting points as inExample 8is to use a formula. If A is (a 1 ,a 2 ) and B is (b 1 ,b 2 ) then ¡! AB= μ b 1 ...

4 If A is at(3,4), B is at(¡ 1 ,2), and C is at(2,¡1), find: a ¡! OA b ¡! AB c ¡! CO d ¡! BC e ¡! CA VECTOR ADDITION Consider ad ...

ZERO VECTOR The zero vector is 0 = μ 0 0 ¶ : For any vectora: a+ 0 = 0 +a= 0. a+(¡a)=(¡a)+a= 0. VECTOR SUBTRACTION To subtract o ...

EXERCISE 24E.2 1 If a= μ 2 ¡ 3 ¶ , b= μ 3 ¡ 1 ¶ , c= μ ¡ 2 ¡ 3 ¶ find: a a+b b b+a c b+c d c+b e a+c f c+a g a+a h b+a+c 2 Given ...

8 Find the two values forkfor which v= μ k 3 ¶ and jvj=5: 9 u= μ k k ¶ and v= μ k+2 1 ¶ are two vectors. a Findkgiven that juj=j ...

We can now check the results ofExample 13algebraically: Ina, 2 r+s=2 μ 3 2 ¶ + μ 2 ¡ 2 ¶ = μ 6 4 ¶ + μ 2 ¡ 2 ¶ = μ 8 2 ¶ and inb ...

Notice that a= μ 6 3 ¶ and b= μ 2 1 ¶ are such that a=3b. We can see that akb. Notice also that jaj= p 36 + 9 = p 45 =3 p 5 =3jb ...

5 A(2,3),B(¡ 1 ,5),C(¡ 1 ,1) and D(¡ 7 ,5) are four points in the Cartesian plane. a Find ¡! AB and ¡! CD: b Explain why ¡! CD i ...

Example 17 Self Tutor In the diagram, ¡! AB=p and ¡! BC=q, M is the midpoint of AB and N divides BC in the ratio1:2. Find in ter ...

5 A, M and B are collinear and M is the midpoint of AB. If a= ¡! OA and b= ¡! OB, show that ¡¡! OM=^12 a+^12 b. 6 In the given f ...

3 Draw a vector diagram to represent a velocity vector of 50 km/h in a NE direction. 4 An aeroplane is flying in an easterly dir ...

Review set 24B #endboxedheading 1 On grid paper draw the vectors: a p= μ 1 4 ¶ b q= μ ¡ 3 ¡ 1 ¶ c r= μ 5 ¡ 2 ¶ 2 Write in the fo ...

Challenge #endboxedheading 12 Use vectors to find the remaining vertex of: 13 In the given figure, O is the origin and OUWV is a ...

Probability 25 Contents: A Introduction to probability [10.1] B Estimating probability [10.2, 10.6] C Probabilities from two-way ...

Consider these statements: “The Wildcats will probably beat the Tigers on Saturday.” “It is unlikely that it will rain today.” “ ...

The probability line below shows words which can be used to describe the chance of an event occurring. EXERCISE 25A 1 Assign sui ...

Therelative frequencyof an event is an estimate of itsprobability. We write estimated P(end)¼ 0 : 148 and estimated P(side)¼ 0 : ...